Multi-resolution dynamic mode decomposition and fast reconstruction method and device for gas-solid system

Abstract

This invention discloses a method and apparatus for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems. The method includes: generating gas-solid flow data samples at multiple time points using CFD-DEM; performing multi-resolution dynamic mode decomposition based on the gas-solid flow data samples; in a layer-by-layer recursive decomposition process, performing mode decomposition on the data samples to be decomposed at the current decomposition layer to obtain the slow and fast modes of the current decomposition layer; and continuing mode decomposition at the next decomposition layer based on the fast modes of the current decomposition layer until the slow and fast modes of each decomposition layer are obtained; and obtaining the overall flow field reconstruction result based on the slow modes of each decomposition layer. This invention decomposes complex gas-solid flow fields into hierarchical combinations of multi-resolution time-scale components through multi-resolution dynamic mode decomposition, which is beneficial for improving the processing efficiency of the gas-solid system flow field reconstruction process and enabling the overall flow field reconstruction result to reflect the flow field change information corresponding to different decomposition layers.

Description

Technical Field

[0001] This invention relates to the field of gas-solid two-phase flow system research and application, and more specifically, to a method and apparatus for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems. Background Technology

[0002] Gas-solid two-phase flow systems are widely used in industrial equipment such as fluidized bed reactors, gas-solid conveying devices, fluidized bed boilers, and particle reactors. In these systems, the gas interacts with a large number of solid particles, and the particle phase exhibits a complex motion state under the influence of the airflow. Non-uniform flow structures such as particle agglomeration and bubbles are prone to occur within the system. These flow structures affect momentum transfer, heat and mass transfer, and reaction processes between the gas and solid phases. Therefore, characterizing the complex flow field distribution and its evolution over time within gas-solid two-phase flow systems is of great significance for flow analysis, operational evaluation, and structural optimization of multiphase flow reactors.

[0003] Currently, the acquisition and analysis of gas-solid two-phase flow characteristics can typically be achieved through experimental measurements or numerical calculations. Experimental measurement methods can obtain some local flow information, but are often limited by factors such as measurement location, sensor placement, the transparency of the experimental setup, and the measurement range, making it difficult to obtain complete flow field information within the gas-solid system. Numerical calculation methods can obtain a relatively complete flow field distribution, but gas-solid two-phase flow systems typically generate large-scale flow field data due to the large number of particles and complex interphase interactions. When analyzing the flow field evolution at multiple time points, or when repeatedly reviewing, post-processing, and comparing large amounts of flow field data, directly relying on the full flow field data for processing and reconstruction is inefficient.

[0004] In gas-solid two-phase flow analysis, in addition to obtaining the flow results at a specific moment, it is often necessary to reconstruct or approximate the flow field state at different moments based on existing flow field data in order to quickly observe changes in physical fields such as solids content, velocity field, and pressure field. For example, when analyzing the internal flow structure of a multiphase reactor, comparing the flow state at different time periods, or visualizing and post-processing large-scale flow field data, it is generally desirable to obtain a relatively complete overall flow field reconstruction result with low data processing volume and high computational efficiency.

[0005] However, the non-uniform structures in gas-solid two-phase flow systems exhibit strong time-varying and localized characteristics, making the flow field changes quite complex. Existing flow field data processing or reconstruction methods, when applied to gas-solid two-phase flow systems, often struggle to achieve a good balance between reconstruction efficiency and the accuracy of depicting complex flow structures, easily leading to problems such as heavy computational or data processing burdens and insufficient reflection of local non-uniform structures in the reconstruction results.

[0006] Therefore, how to improve the efficiency of flow field reconstruction in gas-solid two-phase flow systems and make the reconstruction results better reflect the complex changing characteristics in the gas-solid flow field remains a problem to be solved in this field. Summary of the Invention

[0007] In order to solve at least one of the technical problems in the background art, the present invention proposes a method and apparatus for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems.

[0008] One aspect of the present invention provides a method for multi-resolution dynamic mode decomposition and fast reconstruction of a gas-solid system, the method comprising: The CFD-DEM method is used to generate gas-solid flow data samples of a gas-solid system at multiple time points. The gas-solid flow data samples include gas-solid flow information of each computation grid. Multi-resolution dynamic mode decomposition is performed based on the gas-solid flow data samples. During the layer-by-layer recursive decomposition process, mode decomposition is performed on the data samples to be decomposed in the current decomposition layer to obtain the slow mode and fast mode of the current decomposition layer. The slow mode of the current decomposition layer is retained for subsequent flow field reconstruction. If the recursion termination condition is not met, the data samples to be decomposed in the next decomposition layer are formed based on the fast mode of the current decomposition layer to continue the mode decomposition of the next decomposition layer until the slow mode and fast mode of each decomposition layer are obtained. The flow field of the gas-solid system is reconstructed based on the slow mode of each decomposition layer to obtain the overall flow field reconstruction result of the gas-solid system.

[0009] Optionally, the multi-resolution dynamic mode decomposition based on the gas-solid flow data samples involves performing mode decomposition on the data samples to be decomposed in the current decomposition layer during the layer-by-layer recursive decomposition process. This yields the slow and fast modes of the current decomposition layer. The slow modes of the current decomposition layer are retained for subsequent flow field reconstruction. If the recursion termination condition is not met, the data samples to be decomposed in the next decomposition layer are formed based on the fast modes of the current decomposition layer to continue the mode decomposition of the next decomposition layer, until the slow and fast modes of each decomposition layer are obtained. The flow field of the gas-solid system is reconstructed based on the slow modes of each decomposition layer to obtain the overall reconstructed flow field result of the gas-solid system, including: Based on the gas-solid flow data samples, a first snapshot matrix and a second snapshot matrix with a misalignment relationship between adjacent time moments are constructed, and dynamic mode decomposition is performed based on the first snapshot matrix and the second snapshot matrix to obtain the first slow mode and the first fast mode. The first fast mode is used as the initial data sample to be decomposed and recursively dynamic mode decomposition is performed layer by layer. In the process of recursively dynamic mode decomposition, for each data sample to be decomposed in the current decomposition layer, the data sample to be decomposed is divided into two sub-data samples according to the time window, and dynamic mode decomposition is performed on each sub-data sample to obtain the slow mode and fast mode of the current layer corresponding to each sub-data sample. Each fast mode of the current layer is used as the data sample to be decomposed in the next decomposition layer. By combining the slow modes of each layer, the overall flow field reconstruction result of the gas-solid system is obtained.

[0010] Optionally, the plurality of times are M sampling times arranged consecutively according to a preset unit time step; The construction of a first snapshot matrix and a second snapshot matrix with a misalignment relationship between adjacent time points based on the gas-solid flow data samples includes: The gas-solid flow information of each computational grid at each sampling time is arranged in the same grid order to form the corresponding flow field snapshot vector; In chronological order, the flow field snapshot vectors corresponding to the first sampling time to the (M-1)th sampling time are used to form the first snapshot matrix, and the flow field snapshot vectors corresponding to the second sampling time to the Mth sampling time are used to form the second snapshot matrix.

[0011] Optionally, the step of performing dynamic mode decomposition based on the first snapshot matrix and the second snapshot matrix to obtain the first layer of slow modes and the first layer of fast modes includes: Singular value decomposition is performed on the first snapshot matrix to obtain the POD mode matrix, singular value matrix, and right singular vector matrix; Based on the conjugate transpose of the POD modality matrix, the second snapshot matrix, the right singular vector matrix, and the inverse of the singular value matrix, determine the projection matrix of the operator matrix representing the linear mapping relationship between the first snapshot matrix and the second snapshot matrix in the POD modality space; The projection matrix is ​​subjected to eigenvalue decomposition to obtain the eigenvector matrix and the eigenvalue diagonal matrix of the projection matrix; Based on the eigenvector matrix of the projection matrix, and combined with the inverse matrices of the second snapshot matrix, the right singular vector matrix, and the singular value matrix, the eigenvector matrix of the operator matrix is ​​determined, and the eigenvalue diagonal matrix of the operator matrix is ​​determined based on the eigenvalue diagonal matrix of the projection matrix, thereby obtaining the eigenvalue decomposition of the operator matrix. The dynamic mode decomposition expression is obtained based on the eigenvalue decomposition of the operator matrix. According to the preset mode partitioning method, the modes in the dynamic mode decomposition expression are divided into slow mode parts and fast mode parts. The slow mode parts are determined as the first layer of slow modes, and the fast mode parts are determined as the first layer of fast modes.

[0012] Optionally, the step of using the first-layer fast mode as the initial data sample to be decomposed for layer-by-layer recursive dynamic mode decomposition, wherein during the layer-by-layer recursive dynamic mode decomposition process, for each data sample to be decomposed in the current decomposition layer, the data sample to be decomposed is divided into two sub-data samples according to a time window, and dynamic mode decomposition is performed on each sub-data sample to obtain the slow mode and fast mode of the current layer corresponding to each sub-data sample, and each fast mode of the current layer is used as the data sample to be decomposed in the next decomposition layer, includes: The first fast mode is used as the data sample to be decomposed in the second layer. The data sample to be decomposed in the second layer is divided into two sub-data samples of the second layer according to the time window. Dynamic mode decomposition is performed on the two sub-data samples of the second layer respectively to obtain the second slow mode and the second fast mode corresponding to each of the two sub-data samples of the second layer. The second slow mode corresponding to each of the two sub-data samples of the second layer is retained for subsequent flow field reconstruction. If the recursion termination condition is not met, the second fast mode corresponding to each of the two sub-data samples of the second layer is used as the data sample to be decomposed in the third layer. For the third layer and subsequent layers, for each data sample to be decomposed in the current layer, the data sample to be decomposed is divided into two current layer sub-data samples according to the time window, and dynamic mode decomposition is performed on each current layer sub-data sample to obtain the current layer slow mode and the current layer fast mode corresponding to each current layer sub-data sample. The current layer slow mode corresponding to each current layer sub-data sample is retained for subsequent flow field reconstruction, and if the recursion termination condition is not met, the current layer fast mode corresponding to each current layer sub-data sample is used as the data sample to be decomposed in the next layer.

[0013] Optionally, the combination of slow modes of each layer to obtain the overall flow field reconstruction result of the gas-solid system includes: For each slow mode within each time window of each layer, a corresponding flow field reconstruction term is formed based on the modal amplitude, spatial mode, and temporal evolution term corresponding to the slow mode; The flow field reconstruction terms are superimposed to obtain the overall flow field reconstruction result of the gas-solid system.

[0014] Optionally, the gas-solid system multi-resolution dynamic mode decomposition and fast reconstruction method further includes: The overall flow field reconstruction result is compared with the corresponding gas-solid flow result obtained by the CFD-DEM method, and the accuracy of the overall flow field reconstruction result is determined based on the comparison result. The comparison includes time-averaged physical field comparison and instantaneous physical field comparison. The time-averaged physical field includes at least one of the solids holdup time-averaged field, the mainstream velocity time-averaged field and the gas phase pressure time-averaged field. The instantaneous physical field includes at least one of the solids holdup instantaneous field, the solid phase velocity field along the mainstream direction and the solid phase volume flux field.

[0015] Optionally, the gas-solid flow information includes at least one of solid holdup, average solid velocity, average gas velocity, gas pressure, and solid volumetric flux.

[0016] Optionally, the CFD-DEM method employs an Eulerian-Lagrange method with local mesh refinement for simulation. During the simulation, the Eulerian method is used to solve for gas phase motion characteristics, and the Lagrange method is used to solve for particle motion characteristics. The Eulerian-Lagrange method is coupled using a normalized kernel function method and a particle center-of-mass method, and the normalized kernel function is used to achieve data mapping between the Eulerian-described gas phase computational grid and the Lagrange-described particle grid.

[0017] In another aspect, the present invention provides a device for multi-resolution dynamic mode decomposition and rapid reconstruction of a gas-solid system, the device comprising: The sample forming unit is used to form gas-solid flow data samples of the gas-solid system at multiple time points using the CFD-DEM method. The gas-solid flow data samples include gas-solid flow information of each computation grid. The decomposition and reconstruction unit is used to perform multi-resolution dynamic mode decomposition based on the gas-solid flow data samples. During the layer-by-layer recursive decomposition process, the data samples to be decomposed in the current decomposition layer are decomposed to obtain the slow mode and fast mode of the current decomposition layer. The slow mode of the current decomposition layer is retained for subsequent flow field reconstruction. If the recursion termination condition is not met, the data samples to be decomposed in the next decomposition layer are formed based on the fast mode of the current decomposition layer to continue the mode decomposition of the next decomposition layer until the slow mode and fast mode of each decomposition layer are obtained. The flow field of the gas-solid system is reconstructed based on the slow mode of each decomposition layer to obtain the overall flow field reconstruction result of the gas-solid system.

[0018] To achieve the above objectives, according to another aspect of the present invention, a computer device is also provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction method.

[0019] To achieve the above objectives, according to another aspect of the present invention, a computer-readable storage medium is also provided, on which a computer program / instruction is stored, which, when executed by a processor, implements the steps of the above-described method for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems.

[0020] To achieve the above objectives, according to another aspect of the present invention, a computer program product is also provided, comprising a computer program / instructions that, when executed by a processor, implement the steps of the above-described gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction method.

[0021] The beneficial effects of this invention are as follows: This invention utilizes the CFD-DEM method to generate gas-solid flow data samples of a gas-solid system at multiple time points. Based on these data samples, multi-resolution dynamic mode decomposition is performed. This allows for the acquisition of slow and fast modes at each decomposition layer during the layer-by-layer recursive decomposition process. Furthermore, the invention reconstructs the flow field of the gas-solid system based on the slow modes of each decomposition layer, obtaining the overall reconstructed flow field result. Therefore, this invention can obtain the slow and fast modes of each decomposition layer from the gas-solid flow data samples through multi-resolution dynamic mode decomposition, and can reconstruct the flow field of the gas-solid system based on the slow modes of each decomposition layer. This improves the processing efficiency of the gas-solid system flow field reconstruction process and ensures that the overall reconstructed flow field result reflects the flow field changes corresponding to different decomposition layers. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 This is a flowchart of the multi-resolution dynamic mode decomposition and rapid reconstruction method for gas-solid systems according to an embodiment of the present invention; Figure 2 This is a flowchart of multi-resolution dynamic mode decomposition and reconstruction according to an embodiment of the present invention; Figure 3 This is a flowchart illustrating the generation of a snapshot matrix according to an embodiment of the present invention; Figure 4 This is a flowchart illustrating the determination of the slow and fast modes of the first layer according to an embodiment of the present invention; Figure 5 This is a flowchart illustrating the overall flow field reconstruction result obtained based on the slow modes of each layer in an embodiment of the present invention. Figure 6This is a flowchart illustrating the multi-resolution dynamic mode decomposition approach of an embodiment of the present invention. Figure 7 This is a schematic diagram illustrating the concept of reconstructing the gas-solid full flow field using the multi-resolution dynamic modal method according to an embodiment of the present invention. Figure 8 This is a schematic diagram of the gas-solid bubbling bed structure according to an embodiment of the present invention; Figure 9 This is a first schematic diagram comparing the results of embodiments of the present invention; Figure 10 This is a second schematic diagram comparing the results of embodiments of the present invention; Figure 11 This is a structural block diagram of the gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction device according to an embodiment of the present invention; Figure 12 This is a schematic diagram of a computer device according to an embodiment of the present invention. Detailed Implementation

[0023] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0024] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0025] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products or devices.

[0026] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0027] Gas-solid two-phase flow systems are widely present in industrial production processes. Complex interactions exist between the particulate and gas phases within these systems, easily leading to non-uniform flow structures such as particle agglomeration, bubbles, and localized rarefaction-density distributions. These non-uniform flow structures affect momentum transfer, heat and mass transfer, and reaction processes within the gas-solid system. Therefore, accurately characterizing the spatiotemporal evolution of the flow field in gas-solid systems is crucial for flow analysis and engineering applications. Current technologies, relying solely on traditional numerical calculations to analyze the flow field of gas-solid systems, typically require complete physical governing equations and constitutive relations, resulting in a heavy computational and post-processing burden. Furthermore, the non-uniform structures in gas-solid flow fields exhibit multi-timescale and localized evolutionary characteristics, making it difficult to balance flow field reconstruction efficiency with the representation of complex flow features using single-level / frequency data processing methods.

[0028] Based on this, the present invention proposes a method for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems. By using the CFD-DEM method to form gas-solid flow data samples of the gas-solid system at multiple time points, multi-resolution dynamic mode decomposition is performed based on the gas-solid flow data samples. In the process of layer-by-layer recursive decomposition, the slow mode and fast mode of each decomposition layer are obtained. The lower layer data sample set is reconstructed based on the fast mode, and then the flow field of the gas-solid system is reconstructed based on the slow mode of each decomposition layer, thereby obtaining the overall reconstruction result of the flow field of the gas-solid system.

[0029] Figure 1 This is a flowchart of the multi-resolution dynamic mode decomposition and fast reconstruction method for gas-solid systems according to an embodiment of the present invention, as shown below. Figure 1 As shown, in one embodiment of the present invention, the gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction method of the present invention includes steps S101 and S102.

[0030] Step S101: Use the CFD-DEM method to generate gas-solid flow data samples of the gas-solid system at multiple time points. The gas-solid flow data samples include gas-solid flow information of each computation grid.

[0031] Step S102: Perform multi-resolution dynamic mode decomposition based on the gas-solid flow data samples. During the layer-by-layer recursive decomposition process, perform mode decomposition on the data samples to be decomposed in the current decomposition layer to obtain the slow mode and fast mode of the current decomposition layer. Retain the slow mode of the current decomposition layer for subsequent flow field reconstruction. If the recursion termination condition is not met, form the data samples to be decomposed in the next decomposition layer based on the fast mode of the current decomposition layer to continue the mode decomposition of the next decomposition layer until the slow mode and fast mode of each decomposition layer are obtained. Reconstruct the flow field of the gas-solid system based on the slow mode of each decomposition layer to obtain the overall flow field reconstruction result of the gas-solid system.

[0032] In one embodiment of the present invention, the overall flow field reconstruction result can be the reconstruction value of the gas-solid flow information corresponding to each computational grid within the target sampling time or target time range, and the reconstruction values ​​of each computational grid are arranged according to spatial location to form the corresponding flow field distribution. The gas-solid flow information can include at least one of solid holdup, solid-phase average velocity, gas-phase average velocity, gas-phase pressure, and solid-phase volume flux. Thus, the overall flow field reconstruction result can be represented as the instantaneous field and / or time-averaged field of the corresponding physical quantity, such as the instantaneous solid holdup field, the time-averaged solid holdup field, the mainstream velocity field based on the solid-phase average velocity and / or gas-phase average velocity, the gas-phase pressure field, or the solid-phase volume flux field, etc., used to characterize the flow state and its changes of the gas-solid system within a spatial range.

[0033] In one embodiment of the present invention, step S101 is used to form gas-solid flow data samples required for subsequent decomposition and reconstruction, and step S102 is used to perform modal decomposition and flow field reconstruction based on the gas-solid flow data samples. By combining the CFD-DEM method with multi-resolution dynamic modal decomposition, the present invention can first form gas-solid flow data samples of the gas-solid system at multiple time points based on the CFD-DEM method, then extract modal information of different decomposition layers from the gas-solid flow data samples, and reconstruct the flow field of the gas-solid system based on the slow modes of each decomposition layer. Therefore, based on existing gas-solid flow data samples, the overall flow field reconstruction result of the gas-solid system can be obtained through modal decomposition and slow mode reconstruction, which is beneficial to improving the processing efficiency of the gas-solid system flow field reconstruction process and enabling the overall flow field reconstruction result to reflect the flow field change information corresponding to different decomposition layers.

[0034] In one embodiment of the present invention, the CFD-DEM method refers to a gas-solid two-phase flow simulation method that combines computational fluid dynamics (CFD) and the discrete element method (DEM). CFD describes the motion state of the gas phase within the computational domain, while the DEM describes the motion state of solid particles. Through coupling, gas-solid flow information at multiple time points can be obtained. This gas-solid flow information can be physical quantities characterizing the gas-solid flow field state at each computational grid, including solid content, average solid velocity, and average gas velocity. Therefore, the CFD-DEM method in this invention serves to generate gas-solid flow data samples, providing a data foundation for subsequent multi-resolution dynamic mode decomposition. In one embodiment of the present invention, the CFD-DEM method employs an Eulerian-Lagrange method with local mesh refinement for simulation. During the simulation, the Eulerian method is used to solve for gas phase motion characteristics, and the Lagrange method is used to solve for particle motion characteristics. The Eulerian-Lagrange method coupling employs a normalized kernel function method and a particle centroid method, and the normalized kernel function achieves data mapping between the Eulerian-described gas phase computational grid and the Lagrange-described particle grid.

[0035] In one embodiment of the present invention, multi-resolution dynamic mode decomposition (MMD) is a processing method based on gas-solid flow data samples from multiple time points for mode extraction and recursive decomposition. Dynamic mode decomposition can extract modal components from flow field snapshots at different time points to characterize the dynamic structure of the flow field over time. Multi-resolution dynamic mode decomposition further employs a layer-by-layer recursive decomposition method, using the fast modes obtained in the current layer as data samples to be decomposed in the next decomposition layer, thereby obtaining corresponding slow and fast modes in different decomposition layers. The slow modes can be used for subsequent flow field reconstruction, and the fast modes can be used to continue decomposition to the next layer.

[0036] In one embodiment of the present invention, the gas-solid flow information includes at least one of solid holdup, solid-phase average velocity, gas-phase average velocity, gas-phase pressure, and solid-phase volumetric flux. The solid holdup can represent the volume fraction of solid particles within a corresponding computational grid, characterizing the local distribution of the solid phase within the gas-solid system; the solid-phase average velocity can represent the average velocity of the solid-phase within the corresponding computational grid, and the gas-phase average velocity can represent the average velocity of the gas phase within the corresponding computational grid; both the solid-phase average velocity and the gas-phase average velocity may include velocity components along the main flow direction; the gas-phase pressure can represent the gas-phase pressure within the corresponding computational grid, characterizing the spatial distribution of gas-phase pressure within the gas-solid system; and the solid-phase volumetric flux can characterize the volumetric transport of solid particles during flow.

[0037] In one embodiment of the present invention, based on the gas-solid flow information at multiple sampling times, an instantaneous field and / or a time-averaged field for the corresponding physical quantity can be formed. The instantaneous field can represent the spatial distribution of the corresponding physical quantity in each computational grid at a certain sampling time, and the time-averaged field can represent the time-averaged distribution of the corresponding physical quantity at multiple sampling times. For example, an instantaneous field or a time-averaged field of solid content can be formed based on the non-uniform distribution of particles; an instantaneous field or a time-averaged field of mainstream velocity can be formed based on the mainstream velocity component of the solid phase average velocity and / or the gas phase average velocity; a time-averaged field of gas phase pressure can be formed based on gas phase pressure; and an instantaneous field of solid phase volume flux can be formed based on solid phase volume flux. The above-mentioned gas-solid flow information can serve as the data basis for multi-resolution dynamic mode decomposition and flow field reconstruction, and can also be used for comparison between the flow field reconstruction results and the corresponding gas-solid flow results.

[0038] In one embodiment of the present invention, step S101 is used to generate gas-solid flow data samples of the gas-solid system at multiple time points using the CFD-DEM method. It should be noted that in this invention, the CFD-DEM method is mainly used to characterize the flow characteristics of the gas-solid system and obtain basic gas-solid flow data of the gas-solid system at multiple time points, thereby forming the data samples required for subsequent data-driven analysis and multi-resolution dynamic mode decomposition. The CFD-DEM method itself is not used as a subsequent flow field reconstruction step; the subsequent flow field reconstruction is achieved by performing multi-resolution dynamic mode decomposition on the gas-solid flow data samples and then combining the slow modes of each decomposition layer.

[0039] In one embodiment of the present invention, the governing equations required by the Euler-Lagrange method can be constructed first for the gas-solid two-phase flow system. The CFD-DEM method can be understood as a method that couples computational fluid dynamics with the discrete element method, or as a combination of the Euler and Lagrange methods. The Euler method is mainly used to solve for the gas phase motion characteristics, which can be described by the gas phase mass conservation equation and the gas phase momentum conservation equation. The Lagrange method is mainly used to solve for the particle motion characteristics, which can be characterized by the relationship between single-particle acceleration and force using Newton's laws of motion, and by the relationship between moment of inertia, angular acceleration, and rotational torque using the rigid body rotation law. These characteristics can include particle translational and rotational properties. Specifically, the fluid phase can be described by solving the Navier-Stokes equations, and spatial discretization and time integration are performed using the finite volume method. Simultaneously, the volume fraction correction and momentum exchange generated by the presence of the particle phase are considered, and the momentum exchange can be specifically manifested as gas-solid drag. The granular phase can be simulated using the discrete element method, and the translation and rotation of each particle can be calculated based on Newton's laws of motion combined with the law of rigid body rotation about a fixed axis.

[0040] In one embodiment of the present invention, the mapping relationship between the gas and solid phases can be characterized by the gas-solid drag force relationship. The gas-solid drag forces acting on all particles can be aggregated as the source term of the gas phase momentum conservation equation, and the forces acting on the solid phase can be decomposed one by one to each particle, thereby achieving the closure of solid phase forces. The coupling between the two phases can be achieved through bidirectional data transmission: on the one hand, the force of the fluid field acting on the particles can be calculated through empirical correlations and added as an external force term to the particle motion equation; on the other hand, the volume fraction and momentum loss of the particles can be locally averaged and fed back to the fluid control equation, forming a closed fluid-particle interaction system.

[0041] In one embodiment of the present invention, an Eulerian-Lagrange method with local mesh refinement, coupled with Normalized Kernel Function Method II (NKFMII) and Particle Center-of-Mass Method (PCM), can be employed. By using a normalized kernel function, a data mapping can be achieved between the Eulerian-described gas phase computational grid and the Lagrange-described particle grid, thereby enabling the analysis of gas phase equations with finer meshes. The scale of the finer mesh can even be smaller than the particle diameter, thereby improving the scale resolution of gas phase flow information and obtaining gas-solid flow information with higher spatiotemporal resolution.

[0042] The equation of motion for each particle can be expressed as:

[0043] in, For the mass of a single particle, For single-particle positions, It is time. It is the volume of a single particle. It is the drag coefficient. It's porosity. It is the gas phase pressure gradient. It is the gas phase velocity. It is the velocity of a single particle. It is gravitational acceleration. It is the normal contact force between two particles. It is the tangential contact force between two particles.

[0044] The equation of motion of the particles can be described by the law of rigid body rotation about a fixed axis, and can be specifically expressed as:

[0045] in, It is the moment of inertia. It is the rotational speed of a single particle a. Let the torque be the torque experienced by particle a. It is the radius of a single particle.

[0046] Particle torque can be expressed as:

[0047] in, It is the unit mass of the line connecting the centers of mass of the two particles.

[0048] The normal contact force between two particles can be expressed as:

[0049] in:

[0050] in, The normal overlap is... The particle diameter is and These are the positions of particle b and particle a, respectively. The normal damping coefficient is... e The normal restitution coefficient, This is the stiffness coefficient. Let be the equivalent mass of particle a and particle b. Let be the component of the relative velocity of particle b with respect to particle a in the normal direction.

[0051] The tangential contact force between two particles can be expressed as:

[0052] in:

[0053] in, The coefficient of friction between particles. Particles Relative to particles relative velocity, Let be the component of the relative velocity in the normal direction. Let be the component of the relative velocity in the tangential direction. The tangential damping coefficient is... It is a unit vector in the tangential relative velocity direction.

[0054] The solid volume fraction of grid A can be expressed as:

[0055] in, The solid volume fraction is for grid A. For particle volume, For particle position, The position of grid A, Let c be the position of the grid. Let c be the volume of the grid. Let A be the volume of grid A. For the number of grid cells, For kernel function related parameters, These are parameters related to the supported regions.

[0056] The piecewise cubic kernel function can be expressed as:

[0057] in:

[0058] in, For dimensionless distance parameters, The normalization coefficient is... For the kernel function smoothing length, The cutoff radius for the support region.

[0059] The average particle velocity of grid A can be expressed as:

[0060] in, Let A be the average particle velocity of grid A. For particle velocity, This indicates that the summation is performed on the relevant particles or particles within the support region of grid A.

[0061] The gas-solid drag coefficient of grid A can be expressed as:

[0062] in, Let A be the gas-solid drag coefficient of grid A. Let V be the gas phase velocity at grid A. Let A be the average particle velocity of grid A. The solid volume fraction is for grid A. This indicates that the summation is performed on the relevant particles or particles within the support region of grid A.

[0063] The gas phase mass conservation equation can be expressed as:

[0064] in, Represents porosity. Represents gas density, Represents the gas phase velocity.

[0065] The equation for the conservation of gas phase momentum can be expressed as:

[0066] in, This represents the momentum exchange source term between particles and the gas phase. For gas response force-strain tensor.

[0067] The air-solid drag force can be expressed as:

[0068] in, For grid size, This refers to the total number of particles or the number of particles participating in the calculation of the current grid source term. This is a distribution function or location mapping function related to the particle's location.

[0069] The Gidaspow resistance correlation can be expressed as:

[0070] in, Represents gas viscosity. The drag coefficient, The particle Reynolds number, This represents the volume fraction of the solid phase.

[0071] The gas-response force-strain tensor can be expressed as:

[0072] In one specific embodiment of the present invention, such as Figure 8 As shown, a gas-solid bubbling bed system can be simulated using the CFD-DEM method. This gas-solid bubbling bed system can be considered a typical gas-solid two-phase flow system. Specifically, the CFD-DEM model can be solved by combining the domestically developed industrial software DEMMs (based on a graphics processor) and the open-source fluid dynamics solution software OpenFOAM. DEMMs is a discrete element method software for multi-scale simulation and can be used to solve the main equations of the discrete phase in the CFD-DEM model; OpenFOAM can be used to solve the average Navier-Stokes equations for the gas phase. It should be noted that DEMMs and OpenFOAM are only exemplary implementation platforms; those skilled in the art can also use other software platforms capable of coupled gas-solid two-phase solutions.

[0073] In one specific embodiment of the invention, the length, thickness, and height of the gas-solid bubbling bed are 0.044 m, 0.010 m, and 0.120 m, respectively. Air enters from the bottom of the fluidized bed along the z-direction at an apparent gas velocity of 0.9 m / s, driving the initially stationary spherical particles to begin moving. During stable fluidization, bubbles continuously generate, grow, coalesce, and collapse within the fluidized bed. The CFD-DEM simulation results are in excellent agreement with the direct numerical simulation results, indicating that the CFD-DEM simulation results have sufficient accuracy for data-driven multi-resolution dynamic mode decomposition analysis of multi-scale spatiotemporal coherent structures.

[0074] After completing the CFD-DEM simulation based on the above parameters, the solid content, average solid velocity, and average gas velocity of each grid can be statistically averaged to obtain gas-solid flow information at multiple time points. Data samples from multiple time points can be recorded as a data sample library, serving as gas-solid flow data samples required for subsequent data-driven analysis and multi-resolution dynamic mode decomposition. In this way, gas-solid flow information with high spatiotemporal resolution can be obtained, providing a data foundation for subsequent mode decomposition and flow field reconstruction from flow field snapshots at multiple time points.

[0075] In one specific embodiment of the present invention, the physical and numerical parameters used to simulate a bubbling fluidized bed are shown in Table 1.

[0076] Table 1. Physical and numerical parameters of the simulated bubbling fluidized bed

[0077] like Figure 2 As shown, in one embodiment of the present invention, step S102 above, which involves performing multi-resolution dynamic mode decomposition based on the gas-solid flow data sample, includes the following steps: In the recursive decomposition process, mode decomposition is performed on the data sample to be decomposed in the current decomposition layer to obtain the slow mode and fast mode of the current decomposition layer. The slow mode of the current decomposition layer is retained for subsequent flow field reconstruction. If the recursion termination condition is not met, the data sample to be decomposed in the next decomposition layer is formed based on the fast mode of the current decomposition layer to continue the mode decomposition of the next decomposition layer until the slow mode and fast mode of each decomposition layer are obtained. The flow field of the gas-solid system is reconstructed based on the slow mode of each decomposition layer to obtain the overall flow field reconstruction result of the gas-solid system. Specifically, this includes steps S201 to S203.

[0078] Step S201: Construct a first snapshot matrix and a second snapshot matrix with adjacent time misalignment based on the gas-solid flow data sample, and perform dynamic mode decomposition based on the first snapshot matrix and the second snapshot matrix to obtain the first slow mode and the first fast mode.

[0079] Step S202: The first layer fast mode is used as the initial data sample to be decomposed and recursively dynamic mode decomposition is performed layer by layer. In the process of recursively dynamic mode decomposition, for each data sample to be decomposed in the current decomposition layer, the data sample to be decomposed is divided into two sub-data samples according to the time window, and dynamic mode decomposition is performed on each sub-data sample to obtain the slow mode and fast mode of the current layer corresponding to each sub-data sample. Each fast mode of the current layer is used as the data sample to be decomposed in the next decomposition layer.

[0080] Step S203: Combine the slow modes of each layer to obtain the overall flow field reconstruction result of the gas-solid system.

[0081] In one embodiment of the present invention, steps S201 to S203 are used to further realize multi-resolution dynamic mode decomposition and reconstruction of the gas-solid system flow field based on the gas-solid flow data samples formed in step S101. The gas-solid flow data samples may include flow field data at multiple consecutive sampling times, and the flow field data at each sampling time can be considered as a flow field snapshot. The first snapshot matrix and the second snapshot matrix can be understood as two data matrices formed by staggering the flow field snapshots at adjacent times in chronological order, used to characterize the dynamic evolution relationship of the gas-solid flow field between adjacent times. By performing dynamic mode decomposition based on the first snapshot matrix and the second snapshot matrix, the modal components of the first layer can be extracted from the gas-solid flow data at multiple times, and these modal components can be divided into a first layer of slow modes and a first layer of fast modes.

[0082] In one embodiment of the present invention, slow modes can be understood as modal components that change relatively slowly in the corresponding decomposition layer, suitable for retention and participation in flow field reconstruction; fast modes can be understood as modal components that change relatively quickly in the corresponding decomposition layer, requiring further finer-level decomposition. By using the first layer of fast modes as the initial data sample to be decomposed, and then bisecting the data sample to be decomposed according to a time window in subsequent decomposition layers, corresponding slow and fast modes can be extracted at different time scales and different decomposition layers. The time window can be understood as a data interval formed by dividing the data sample to be decomposed in the time dimension, used to enable dynamic mode decomposition to process flow field changes within different time periods.

[0083] Through the aforementioned layer-by-layer recursive dynamic modal decomposition, this invention can decompose the flow field variation information in gas-solid flow data samples into different decomposition layers and different time windows, and retain the corresponding slow modes in each decomposition layer. Furthermore, by combining the slow modes of each layer, the overall flow field reconstruction result of the gas-solid system can be obtained. Therefore, this invention can extract modal information at different levels using multi-resolution dynamic modal decomposition based on existing gas-solid flow data samples, and realize flow field reconstruction of the gas-solid system based on the slow modes of each layer. This improves the processing efficiency of the flow field reconstruction process and ensures that the overall flow field reconstruction result reflects the flow field variation information corresponding to different decomposition layers.

[0084] In one embodiment of the present invention, the plurality of time points refers to M sampling time points arranged consecutively according to a preset unit time step. The preset unit time step can be set according to the flow change rate of the gas-solid system, the output frequency of the CFD-DEM simulation results, and the time resolution required for subsequent dynamic mode decomposition. For example, in a specific embodiment, a unit time step of 0.001s can be used to select full-field data, and a total of 5001 time points of full flow field data can be obtained as snapshot data required for the first layer of the multi-resolution dynamic mode decomposition method. It should be noted that the above-mentioned unit time step and number of sampling time points are only specific examples, and in actual implementation, they can be adjusted according to the scale of the gas-solid system to be analyzed, computing resources, and reconstruction accuracy requirements.

[0085] like Figure 3 As shown, in one embodiment of the present invention, the construction of a first snapshot matrix and a second snapshot matrix with adjacent time misalignment based on the gas-solid flow data sample in step S201 includes steps S301 and S302.

[0086] Step S301: Arrange the gas-solid flow information of each computational grid at each sampling time into the corresponding flow field snapshot vector according to the same grid order.

[0087] In one embodiment of the present invention, the flow field snapshot vector is used to represent the full flow field state of the gas-solid system at a certain sampling time. Specifically, at each sampling time, the gas-solid flow information corresponding to each computational grid can be extracted sequentially according to a preset consistent grid order, and the gas-solid flow information of each computational grid can be arranged into a column vector to obtain the flow field snapshot vector corresponding to that sampling time. The preset consistent grid order can be the numbering order of the computational grids, the spatial coordinate order, or other arrangement order that can remain consistent across different sampling times. By using the same grid order at different sampling times, elements at the same position in different flow field snapshot vectors can correspond to the same computational grid or the same physical quantity in the same computational grid, thereby ensuring that the subsequent snapshot matrix can correctly reflect the change relationship of the gas-solid flow field over time.

[0088] In one embodiment of the present invention, the gas-solid flow information may include physical quantities such as solid holdup, average solid velocity, and average gas velocity. At each sampling time, one or more types of gas-solid flow information in each computational grid can be arranged according to the same grid order to form a corresponding flow field snapshot vector. For example, the flow field snapshot vector corresponding to the i-th sampling time can be denoted as... , It can be composed of gas-solid flow information output in an ordered manner according to the data within the grid in the i-th flow field snapshot. Thus, the flow field snapshot vectors at multiple sampling times can form time series data for dynamic mode decomposition.

[0089] Step S302: According to the time sequence, the flow field snapshot vectors corresponding to the first sampling time to the (M-1)th sampling time are used to form the first snapshot matrix, and the flow field snapshot vectors corresponding to the second sampling time to the Mth sampling time are used to form the second snapshot matrix.

[0090] In one embodiment of the present invention, the flow field snapshot vectors corresponding to the first sampling time to the (M-1)th sampling time can be arranged in chronological order to form a first snapshot matrix, and the flow field snapshot vectors corresponding to the second sampling time to the Mth sampling time can be arranged to form a second snapshot matrix. The first snapshot matrix can be represented as:

[0091] The second snapshot matrix can be represented as:

[0092] in, Let represent the flow field snapshot vector corresponding to the i-th sampling time, and M represent the total number of sampling times. As can be seen from the above construction method, there is a unit time step misalignment between the first snapshot matrix and the second snapshot matrix. That is, columns 1 to M-1 of the first snapshot matrix correspond to the flow field snapshot vectors from the 1st sampling time to the M-1th sampling time, respectively, and columns 1 to M-1 of the second snapshot matrix correspond to the flow field snapshot vectors from the 2nd sampling time to the Mth sampling time, respectively.

[0093] In one embodiment of the present invention, a first snapshot matrix and a second snapshot matrix with a misalignment relationship between adjacent time points are constructed to describe the evolution relationship of the gas-solid flow field between adjacent sampling time points during subsequent dynamic mode decomposition. Combined with the dynamic mode decomposition method, a linear mapping relationship can be assumed between consecutive time snapshots, and thus, a linear mapping relationship can be approximated between the first snapshot matrix and the second snapshot matrix. Based on this linear mapping relationship, singular value decomposition, projection matrix construction, and eigenvalue decomposition can be further performed in subsequent steps to obtain modal information characterizing the dynamic evolution features of the gas-solid flow field.

[0094] like Figure 4 As shown, in one embodiment of the present invention, the dynamic mode decomposition based on the first snapshot matrix and the second snapshot matrix in step S201 above to obtain the first slow mode and the first fast mode includes steps S401 to S405.

[0095] Step S401: Perform singular value decomposition on the first snapshot matrix to obtain the POD mode matrix, singular value matrix and right singular vector matrix.

[0096] Step S402: Based on the conjugate transpose of the POD modality matrix, the second snapshot matrix, the right singular vector matrix, and the inverse of the singular value matrix, determine the projection matrix of the operator matrix representing the linear mapping relationship between the first snapshot matrix and the second snapshot matrix in the POD modality space.

[0097] Step S403: Perform eigenvalue decomposition on the projection matrix to obtain the eigenvector matrix and the eigenvalue diagonal matrix of the projection matrix.

[0098] Step S404: Based on the eigenvector matrix of the projection matrix, and combined with the inverse matrices of the second snapshot matrix, the right singular vector matrix, and the singular value matrix, determine the eigenvector matrix of the operator matrix, and determine the eigenvalue diagonal matrix of the operator matrix based on the eigenvalue diagonal matrix of the projection matrix, thereby obtaining the eigenvalue decomposition of the operator matrix.

[0099] Step S405: Obtain the dynamic mode decomposition expression based on the eigenvalue decomposition of the operator matrix. According to the preset mode partitioning method, divide the modes in the dynamic mode decomposition expression into a slow mode part and a fast mode part. The slow mode part is determined as the first layer slow mode, and the fast mode part is determined as the first layer fast mode.

[0100] In one embodiment of the present invention, steps S401 to S405 are used to perform a first-level dynamic mode decomposition based on the first snapshot matrix and the second snapshot matrix to obtain a first-level slow mode and a first-level fast mode. It should be noted that the basic idea of ​​dynamic mode decomposition is that for multiple flow field snapshots arranged in chronological order, an approximate linear mapping relationship exists between flow field snapshots at adjacent times. Based on this approximate linear mapping relationship, modal components characterizing the flow field evolution process can be extracted from gas-solid flow data at multiple times.

[0101] In one embodiment of the present invention, it is assumed that the flow field snapshot vector corresponding to the j-th sampling time is The linear mapping relationship between adjacent sampling times can be expressed as:

[0102] Where A represents the operator matrix to be determined, which is used to characterize the linear mapping relationship between flow field snapshot vectors at adjacent sampling times. Since the first snapshot matrix and the second snapshot matrix are respectively composed of flow field snapshot vectors that are misaligned at adjacent times, the linear mapping relationship between the first snapshot matrix and the second snapshot matrix can be expressed as:

[0103] in, This represents the first snapshot matrix. Let A represent the second snapshot matrix. It should be noted that the operator matrix A typically has a large dimension, and directly solving for and performing eigenvalue decomposition on operator matrix A would be computationally intensive. Therefore, this invention constructs a projection matrix in the dimensionality-reduced POD mode space using singular value decomposition and POD mode space projection, and performs dynamic mode decomposition based on the projection matrix.

[0104] In step S401, singular value decomposition is performed on the first snapshot matrix to obtain the POD mode matrix, singular value matrix, and right singular vector matrix. Specifically, the singular value decomposition of the first snapshot matrix can be expressed as:

[0105] Where U is the left singular vector matrix, also known as the POD mode matrix; Σ is the singular value matrix; and V is the right singular vector matrix. This represents the conjugate transpose of the right singular vector matrix. The POD mode matrix U can be used to characterize the low-dimensional subspace containing the main spatial structure in the first snapshot matrix. By performing singular value decomposition on the first snapshot matrix, a foundation can be provided for subsequently projecting the operator matrix onto the POD mode space.

[0106] In one embodiment of the present invention, based on the linear mapping relationship between the first snapshot matrix and the second snapshot matrix, and the singular value decomposition result of the first snapshot matrix, the form of the operator matrix A to be determined can be obtained as follows:

[0107] in, This represents the inverse or truncated inverse of the singular value matrix Σ. This represents the conjugate transpose of the POD mode matrix U. It should be noted that in practical implementation, the singular value decomposition results can be truncated based on the magnitude of the singular values ​​to retain the modal components that contribute significantly to the main changes in the flow field, thereby reducing computational load and noise impact.

[0108] In step S402, based on the conjugate transpose of the POD mode matrix, the second snapshot matrix, the right singular vector matrix, and the inverse of the singular value matrix, the projection matrix of the operator matrix representing the linear mapping relationship between the first snapshot matrix and the second snapshot matrix in the POD mode space is determined. Specifically, the projection matrix can be expressed as:

[0109] Here, à represents the projection matrix of operator matrix A in the POD mode space. Since the dimension of the projection matrix à is smaller than the dimension of the original operator matrix A, performing subsequent eigenvalue decomposition on the projection matrix à can reduce the computational complexity in the dynamic mode decomposition process.

[0110] In step S403, the projection matrix is ​​subjected to eigenvalue decomposition to obtain the eigenvector matrix and the eigenvalue diagonal matrix of the projection matrix. Specifically, the eigenvalue decomposition of the projection matrix can be expressed as:

[0111] Where W is the eigenvector matrix composed of the eigenvectors of the projection matrix Ã, and Λ is the eigenvalue diagonal matrix composed of the eigenvalues ​​of the projection matrix à arranged sequentially on the diagonal. Each eigenvalue in the eigenvalue diagonal matrix Λ is used to characterize the evolution of the corresponding mode over time, and the eigenvector matrix W is used to characterize the characteristic directions in the POD mode space.

[0112] In step S404, based on the eigenvector matrix of the projection matrix and combined with the inverse matrices of the second snapshot matrix, the right singular vector matrix, and the singular value matrix, the eigenvector matrix of the operator matrix is ​​determined, and the eigenvalue diagonal matrix of the operator matrix is ​​determined based on the eigenvalue diagonal matrix of the projection matrix, thereby obtaining the eigenvalue decomposition of the operator matrix. Specifically, according to matrix properties, the eigenvalues ​​of operator matrix A can be determined by the eigenvalues ​​of projection matrix A, therefore the eigenvalue diagonal matrix of operator matrix A can still be Λ; the dynamic mode corresponding to operator matrix A, i.e., the eigenvector matrix, can be expressed as:

[0113] Here, Ψ represents the dynamic mode matrix, and each column of Ψ represents a dynamic mode. Therefore, based on the eigenvalues ​​of the projection matrix, the eigenvalues ​​and dynamic modes corresponding to the original operator matrix A can be obtained, thus completing the dynamic mode decomposition of the first layer of data.

[0114] In step S405, the dynamic mode decomposition expression is obtained based on the eigenvalue decomposition of the operator matrix. Specifically, for any time t, the flow field state of the gas-solid system can be expressed by the dynamic mode decomposition expression as follows:

[0115] Or it can be represented in matrix form:

[0116] in, This represents the dynamic mode decomposition and reconstruction result corresponding to time t; Let ξ represent the k-th spatial mode and ξ represent the spatial coordinates. represents the modal amplitude of the k-th mode at the initial time; b represents the amplitude vector composed of the amplitudes of all modes; This represents the time evolution parameter corresponding to the k-th mode; This represents a diagonal matrix composed of the time evolution terms of each mode.

[0117] The modal amplitude vector b can be determined based on the initial flow field snapshot vector and the dynamic mode matrix, such as:

[0118] in Represents the pseudo-inverse of the dynamic mode matrix Ψ. This represents the flow field snapshot vector corresponding to the first sampling time.

[0119] In one embodiment of the present invention, the modes in the dynamic mode decomposition expression can be divided into slow mode components and fast mode components according to a preset mode partitioning method. Specifically, the dynamic mode decomposition expression can be expressed as the sum of the slow mode components and the fast mode components:

[0120] The first part It can be used as the slow modal component, the latter part. This can be considered as the fast modal component, where m is a preset modal partitioning parameter used to determine the boundary between the slow modal component and the fast modal component. In one embodiment of the present invention, the modal partitioning parameter m for the first layer decomposition can be selected as a preset proportion of the total number of sampling times M, for example, M / 2.

[0121] In one specific implementation, modes that change relatively slowly or at relatively low frequencies can be defined as slow modes, while modes that change relatively quickly or at relatively high frequencies can be defined as fast modes. That is, slow modes can correspond to low-frequency data or background states, while fast modes can correspond to high-frequency data or rapidly changing components.

[0122] In one embodiment of the present invention, the first-layer slow modes can be retained and used for subsequent flow field reconstruction, while the first-layer fast modes can serve as the initial data samples to be decomposed in subsequent layer-by-layer recursive dynamic mode decomposition. Through this method, the present invention can extract both slow-changing and fast-changing modes from the gas-solid flow field data during the first-layer dynamic mode decomposition process, providing a foundation for subsequent multi-level, multi-time-window dynamic mode decomposition and flow field reconstruction.

[0123] In one embodiment of the present invention, step S202 above, which uses the first-layer fast mode as the initial data sample to be decomposed for layer-by-layer recursive dynamic mode decomposition, involves, during the layer-by-layer recursive dynamic mode decomposition process, dividing each data sample to be decomposed in the current decomposition layer into two sub-data samples according to a time window, and performing dynamic mode decomposition on each sub-data sample to obtain the slow mode and fast mode corresponding to each sub-data sample in the current layer, and using each fast mode of the current layer as the data sample to be decomposed in the next decomposition layer, includes: The first fast mode is used as the data sample to be decomposed in the second layer. The data sample to be decomposed in the second layer is divided into two sub-data samples of the second layer according to the time window. Dynamic mode decomposition is performed on the two sub-data samples of the second layer respectively to obtain the second slow mode and the second fast mode corresponding to each of the two sub-data samples of the second layer. The second slow mode corresponding to each of the two sub-data samples of the second layer is retained for subsequent flow field reconstruction. If the recursion termination condition is not met, the second fast mode corresponding to each of the two sub-data samples of the second layer is used as the data sample to be decomposed in the third layer. For the third layer and subsequent layers, for each data sample to be decomposed in the current layer, the data sample to be decomposed is divided into two current layer sub-data samples according to the time window, and dynamic mode decomposition is performed on each current layer sub-data sample to obtain the current layer slow mode and the current layer fast mode corresponding to each current layer sub-data sample. The current layer slow mode corresponding to each current layer sub-data sample is retained for subsequent flow field reconstruction, and if the recursion termination condition is not met, the current layer fast mode corresponding to each current layer sub-data sample is used as the data sample to be decomposed in the next layer.

[0124] In one embodiment of the present invention, step S202 is used to perform a layer-by-layer recursive dynamic mode decomposition on the first-layer fast mode, based on the first-layer dynamic mode decomposition. Through this step, the rapidly changing components in the gas-solid flow data sample can be further decomposed into different time windows and different decomposition layers, thereby obtaining the slow and fast modes corresponding to different layers. The layer-by-layer recursive dynamic mode decomposition can be understood as follows: in each decomposition layer, the slow modes obtained from the dynamic mode decomposition of that layer are retained for subsequent flow field reconstruction, and the fast modes obtained from that layer are used as the data samples to be decomposed in the next decomposition layer for further decomposition.

[0125] like Figure 6 As shown, the data snapshot library can consist of flow field snapshots corresponding to multiple consecutive sampling times. Figure 6The diagram above illustrates the data snapshot libraries in different decomposition layers. As the number of decomposition layers increases, the data samples to be decomposed in the current layer can be divided into shorter sub-data samples according to the time window. For example, the data snapshot library of the first layer can be further divided into the corresponding sub-data snapshot libraries of the second and third layers. Figure 6 The diagram below illustrates the modal distribution and frequency-time relationship corresponding to each decomposition layer. Dividing the data sample to be decomposed along the time direction allows subsequent dynamic modal decomposition to process flow field changes within a shorter time window. Along the frequency direction, slow modes correspond to modal components that change relatively slowly, while fast modes correspond to modal components that change relatively quickly. Figure 6 The region where the modes are removed can be understood as the slow mode region separated from the data to be further decomposed in the current decomposition layer. This slow mode is not deleted from the final reconstruction result, but is retained for subsequent flow field reconstruction. The fast modes that are not retained as slow modes continue to be used as data samples to be decomposed in the next decomposition layer.

[0126] In one embodiment of the present invention, after the first-level dynamic mode decomposition, the dynamic mode decomposition result of the first-level data can be divided into a slow-mode component and a fast-mode component. The slow-mode component can be retained and used for subsequent reconstruction, while the fast-mode component can form a second-level data sample and serve as the initial data sample to be decomposed in the layer-by-layer recursive dynamic mode decomposition. Specifically, the second-level data sample formed from the first-level fast mode can be represented as:

[0127] in, This represents the data sample to be decomposed in the second layer, formed by the fast modes of the first layer; m is the preset partitioning parameter between the slow and fast modes; M is the total number of modes in the dynamic mode decomposition expression of the first layer.

[0128] It should be noted that, Figure 6 In , , This is used to illustrate the data snapshot library corresponding to different decomposition layers or different time windows. It indicates that as the time window is divided, the data samples to be decomposed are refined layer by layer on the time scale. It is not used to limit the data matrix to only have the specific size shown in the figure.

[0129] In one embodiment of the present invention, after forming the data sample to be decomposed in the second layer, the data sample to be decomposed can be divided into two sub-data samples according to a time window. This division process can be represented as:

[0130] in, and These represent the two sub-data samples obtained after dividing the second-level data sample into two parts according to a time window. The "+" in the above expression indicates that the second-level data sample is composed of sub-data samples corresponding to the two time windows, and is not limited to a simple numerical addition relationship. By dividing according to a time window, subsequent dynamic mode decomposition can process the fast mode data in different time periods, thereby further extracting the slow-changing and fast-changing components within different time windows.

[0131] In one embodiment of the present invention, after obtaining two sub-data samples, they can be processed separately. and Perform dynamic mode decomposition. For each sub-data sample, the dynamic mode decomposition process described in steps S401 to S405 above can be followed to construct the corresponding adjacent time-time misaligned snapshot matrix, perform singular value decomposition, projection matrix construction, projection matrix eigenvalue decomposition, and dynamic mode expression construction, and further divide the slow mode and fast mode within the time window.

[0132] In one embodiment of the invention, for the two time windows in the second layer, the relatively slower-changing modes within each time window can be retained. For example, the slowest mode within each of the two time windows can be retained. One mode is retained as a second-level slow mode, wherein the second-level slow mode can be derived from... express, This represents the spatial modes obtained from the second-level dynamic mode decomposition. This indicates the number of slow modes that are pre-reserved in the second layer. These second-layer slow modes can be used as part of subsequent flow field reconstruction.

[0133] In one embodiment of the present invention, the fast modes obtained from the second-level dynamic mode decomposition can be used as data samples to be decomposed in the next decomposition layer. That is, when constructing the data snapshot matrix of the next level, the slow modes of the current layer are no longer used as data to be decomposed in the next layer, but are retained for subsequent flow field reconstruction; the fast modes of the current layer are retained to form data samples to be decomposed in the next layer, and are again divided according to the time window, and then dynamic mode decomposition is performed on the sub-data samples after the division to continue the sorting of fast and slow modes.

[0134] In one embodiment of the present invention, the above recursive process can be repeated sequentially. For each data sample to be decomposed in any current decomposition layer, the data sample to be decomposed can be divided into two sub-data samples according to a time window, and dynamic mode decomposition is performed on each sub-data sample to obtain the current layer slow mode and the current layer fast mode corresponding to each sub-data sample; wherein, the current layer slow mode is retained and used for subsequent reconstruction, and the current layer fast mode is used as the data sample to be decomposed in the next decomposition layer. Thus, as the number of decomposition layers gradually increases, multiple decomposition layers and multiple slow and fast modes under multiple time windows can be formed.

[0135] In one embodiment of the present invention, through the above-described layer-by-layer recursive dynamic mode decomposition, the fast-changing components in the gas-solid flow field data can be further decomposed into finer time windows, and the corresponding slow modes can be extracted at different time and frequency levels. Compared with the method of performing dynamic mode decomposition only once on the entire time series, this layer-by-layer recursive decomposition method is beneficial for further extraction and analysis of effective information in the fast modes, and is beneficial for improving the ability of the subsequent overall flow field reconstruction results to characterize the spatiotemporal coherence structure of the gas-solid flow field.

[0136] In one embodiment of the present invention, for each sub-data sample in the current decomposition layer, dynamic mode decomposition is performed on the sub-data sample to obtain the current layer slow mode and the current layer fast mode corresponding to the sub-data sample, including: Based on the sub-flow field snapshot vectors corresponding to multiple sampling times in the sub-data sample, construct the current preceding snapshot matrix and the current following snapshot matrix with adjacent time misalignment relationships; Perform singular value decomposition on the current previous snapshot matrix to obtain the current POD mode matrix, the current singular value matrix, and the current right singular vector matrix; Based on the conjugate transpose of the current POD mode matrix, the current subsequent snapshot matrix, the current right singular vector matrix, and the inverse of the current singular value matrix, determine the current projection matrix of the current operator matrix in the current POD mode space that represents the linear mapping relationship between the current preceding snapshot matrix and the current subsequent snapshot matrix. Perform eigenvalue decomposition on the current projection matrix to obtain the current eigenvector matrix and the current eigenvalue diagonal matrix of the current projection matrix; Based on the current eigenvector matrix of the current projection matrix, and combined with the current post-single snapshot matrix, the current right singular vector matrix, and the inverse of the current singular value matrix, the current eigenvector matrix of the current operator matrix is ​​determined, and based on the current eigenvalue diagonal matrix of the current projection matrix, the current eigenvalue diagonal matrix of the current operator matrix is ​​determined, thereby obtaining the eigenvalue decomposition of the current operator matrix; The current dynamic mode decomposition expression corresponding to the sub-data sample is obtained by eigenvalue decomposition of the current operator matrix, and the modes in the current dynamic mode decomposition expression are divided into the current layer slow mode and the current layer fast mode according to the preset mode partitioning method.

[0137] In specific implementation, the sub-data sample may include flow field data from multiple sampling moments within a corresponding time window. For this sub-data sample, the flow field data corresponding to each sampling moment can be arranged in the same grid order to form a corresponding sub-flow field snapshot vector. The current preceding snapshot matrix can be composed of the sub-flow field snapshot vectors corresponding to the previous group of consecutive sampling moments in this sub-data sample, and the current following snapshot matrix can be composed of the sub-flow field snapshot vectors corresponding to the next group of consecutive sampling moments that are shifted one sampling moment backward relative to the previous group of consecutive sampling moments. Thus, the current preceding snapshot matrix and the current following snapshot matrix can characterize the flow field evolution relationship between adjacent sampling moments of this sub-data sample within the corresponding time window.

[0138] It should be noted that the current preceding snapshot matrix and the current following snapshot matrix are snapshot matrices constructed for the current sub-data samples in the current decomposition layer. Their data originates from the data samples to be decomposed formed by the fast modes of the previous decomposition layer or their time window sub-data samples, and are different from the snapshot matrix constructed based on the original gas-solid flow data samples during the first layer of dynamic mode decomposition. Using the above method, dynamic mode decomposition can be performed on the sub-data samples within each time window in the second and subsequent decomposition layers, retaining the current layer's slow modes, and continuing to use the current layer's fast modes as data samples to be decomposed in the next decomposition layer if the recursion termination condition is not met.

[0139] In one embodiment of the present invention, the preset mode partitioning method can be determined by mode partitioning parameters. For the dynamic mode decomposition expression obtained from the first-level dynamic mode decomposition, a first-level mode partitioning parameter m can be set, and the first-level dynamic mode can be divided into a first-level slow mode and a first-level fast mode according to the first-level mode partitioning parameter m. Specifically, the first-level mode partitioning parameter m can be set according to the number of first-level dynamic modes or the number of sampling times; for example, it can be selected as a preset proportion of the total number of sampling times M.

[0140] In one embodiment of the present invention, corresponding current mode partitioning parameters can be set for sub-data samples in the second decomposition layer and subsequent decomposition layers. Specifically, for sub-data samples within the j-th time window of the l-th layer, the current mode partitioning parameter m can be set. l,j And according to the current mode partitioning parameter m l,jThe modes in the current dynamic mode decomposition expression corresponding to the sub-data sample are divided into the current layer slow mode and the current layer fast mode. The current mode division parameter m... l,j The ratio can be determined based on a preset proportion of the number of dynamic modes corresponding to the sub-data sample, or it can be determined based on a preset proportion of the number of sampling times contained in the sub-data sample.

[0141] In one embodiment of the present invention, when the number of dynamic modes corresponding to the sub-data samples in the j-th time window of the l-th layer is M l,j At that time, the current mode division parameter m l,j M can be selected. l,j The preset ratio, for example, selected as M l,j / 2. Therefore, for sub-data samples in different decomposition layers and different time windows, the mode partitioning parameters can be determined according to the number of modes corresponding to each sub-data sample, instead of using the same mode partitioning parameters for all decomposition layers.

[0142] In one embodiment of the present invention, the layer-by-layer recursive dynamic mode decomposition can end after reaching a preset number of decomposition layers. Specifically, the total number of decomposition layers L can be preset, and dynamic mode decomposition, slow mode retention, fast mode decomposition, and time window bisection processing are performed sequentially starting from the first layer until the dynamic mode decomposition of the Lth layer is completed. After the dynamic mode decomposition of the Lth layer is completed, the fast modes obtained in the Lth layer are no longer used as data samples to be decomposed in the next decomposition layer. Instead, the subsequent flow field reconstruction is performed based on the slow modes obtained from each decomposition layer.

[0143] In this embodiment of the invention, the preset number of decomposition layers L can be set according to the sampling duration, sampling time step, flow field change characteristics, and computational processing requirements of the gas-solid flow data samples. For example, when there are many sampling moments and a finer modal decomposition result is desired within a finer time window, a larger preset number of decomposition layers can be set; when there are few sampling moments or a reduction in computational processing load is desired, a smaller preset number of decomposition layers can be set. Thus, a balance can be struck between the fineness of modal decomposition and the computational load.

[0144] In one embodiment of the present invention, to ensure that the data samples to be decomposed in the current decomposition layer can continue to construct a snapshot matrix of adjacent time-time misalignment relationships, the current data samples to be decomposed should contain sampling time data that can support dynamic mode decomposition. When a data sample to be decomposed can no longer form adjacent time-time snapshot data that meets the requirements of dynamic mode decomposition after being bisected according to a time window, the recursive decomposition of the data sample to be decomposed can be stopped. That is, the layer-by-layer recursive dynamic mode decomposition can end when the preset decomposition layer number L is reached, or the further decomposition of the data sample to be decomposed can be stopped when the data sample to be decomposed no longer meets the conditions for continuing to construct a snapshot matrix.

[0145] By using the aforementioned recursive termination condition, the multi-resolution dynamic modal decomposition process of this invention can have a clear decomposition endpoint, avoiding infinite recursive decomposition. Simultaneously, by presetting the number of decomposition layers and retaining the slow modes of each decomposition layer, subsequent flow field reconstruction can be completed based on a finite number of decomposition layers and time windows, thereby ensuring that the flow field reconstruction process has good feasibility and computational controllability.

[0146] like Figure 5 As shown, in one embodiment of the present invention, the combination of slow modes of each layer in step S203 above to obtain the overall flow field reconstruction result of the gas-solid system includes steps S501 and S502.

[0147] Step S501: For each slow mode in each layer and time window, a corresponding flow field reconstruction term is formed based on the modal amplitude, spatial mode and time evolution term corresponding to the slow mode.

[0148] Step S502: The flow field reconstruction terms are superimposed to obtain the overall flow field reconstruction result of the gas-solid system.

[0149] In one embodiment of the present invention, step S203 is used to combine the slow modes obtained in the layer-by-layer recursive dynamic modal decomposition process to obtain the overall flow field reconstruction result of the gas-solid system. It should be noted that in the aforementioned layer-by-layer recursive dynamic modal decomposition process, the slow modes divided in each decomposition layer are retained and used as components of the subsequent flow field reconstruction; if the recursion termination condition is not met, the fast modes divided in each decomposition layer can be used to continue constructing the data samples to be decomposed in the next decomposition layer. Therefore, after completing the recursive dynamic modal decomposition within a preset number of decomposition layers, the overall flow field reconstruction result of the gas-solid system can be formed based on the slow modes retained in each decomposition layer and each time window.

[0150] Figure 7 This diagram illustrates the concept behind reconstructing the gas-solid full flow field using a multi-resolution dynamic mode decomposition method in an embodiment of the present invention. Figure 7In the diagram, the horizontal axis represents time, and the vertical axis represents frequency. Different rectangular areas are used to illustrate the distribution of slow modes retained under different decomposition levels and time windows in the time-frequency plane. Here, l represents the decomposition level, j represents the time window, and k is used to identify the slow modes participating in reconstruction within the corresponding decomposition level and time window. This represents the spatial mode identified by k within the j-th time pane of the l-th layer.

[0151] from Figure 7 As can be seen in this diagram, the first decomposition layer corresponds to a time pane that covers the entire time range and preserves the slow modes within that time pane, as shown in the figure. The second decomposition layer corresponds to two time panes, and retains the slow modes within each time pane, as shown in the figure. and The third decomposition layer corresponds to four time panes; the fourth decomposition layer corresponds to eight time panes. Therefore, Figure 7 This illustrates that as the decomposition levels increase, the time panes can be refined layer by layer, and the slow modes retained in different decomposition levels and different time panes can collectively serve as the basis for subsequent linear combination reconstruction of the entire gas-solid flow field. It should be noted that... Figure 7 This is only used to illustrate the relationship between time pane division and slow mode retention in multi-resolution dynamic modal decomposition, and is not intended to limit the number of decomposition layers, the number of time panes, or the number of slow modes retained in each time pane in actual implementation.

[0152] In step S501, for each slow mode within each time window of each layer, a corresponding flow field reconstruction term can be formed based on the modal amplitude, spatial mode, and temporal evolution term corresponding to the slow mode. Specifically, the spatial mode is used to characterize the spatial distribution characteristics of the corresponding slow mode; the modal amplitude is used to characterize the contribution of the corresponding slow mode to the reconstruction result; and the temporal evolution term is used to characterize the evolution relationship of the corresponding slow mode over time. Thus, for the k-th slow mode within the j-th time window of the l-th layer, a corresponding flow field reconstruction term can be formed based on the modal amplitude, spatial mode, and temporal evolution term corresponding to the slow mode.

[0153] In one embodiment of the present invention, the flow field reconstruction term formed by the slow modes within each time window of each layer can be expressed as:

[0154] Where l represents the sequence number of the decomposition layer; j represents the sequence number of the time window in the l-th layer; and k represents the sequence number of the slow mode within the corresponding time window. This represents the time window function corresponding to the j-th time window of the l-th layer, used to limit the participation of the corresponding slow mode in reconstruction within the corresponding time window; This represents the modal amplitude corresponding to the k-th slow mode within the j-th time window of the l-th layer; This represents the spatial mode corresponding to the k-th slow mode within the j-th time window of the l-th layer; Represents spatial coordinates; This represents the time evolution parameter corresponding to the k-th slow mode within the j-th time window of the l-th layer; t represents time. It should be noted that the time window function can be determined based on the time window formed during the aforementioned recursive decomposition process, so that the corresponding slow mode participates in flow field reconstruction within its corresponding time window.

[0155] In step S502, the flow field reconstruction terms corresponding to each slow mode within each time window of each layer can be linearly combined or linearly superimposed to obtain the overall flow field reconstruction result of the gas-solid system. Specifically, the multi-resolution dynamic mode decomposition reconstruction result of the gas-solid system can be expressed as:

[0156] in, This represents the multi-resolution dynamic mode decomposition and reconstruction results of a gas-solid system. L Indicates the total number of decomposition layers; J Indicates the number of time windows in the corresponding decomposition layer; This indicates the number of slow modes used for reconstruction within the corresponding layer or time window; the meanings of other parameters are the same as above. As can be seen from the above expression, the overall flow field reconstruction result is formed by a linear combination of the flow field reconstruction terms corresponding to the slow modes retained in different decomposition layers and different time windows.

[0157] In one embodiment of the present invention, the combination of slow modes of each layer can be understood as forming corresponding flow field reconstruction terms from the slow modes retained in each decomposition layer according to their corresponding time windows, modal amplitudes, spatial modes, and temporal evolution terms, and then linearly combining or linearly superimposing these flow field reconstruction terms, rather than directly using fast modes that have not been further decomposed as the final reconstruction terms. Since different decomposition layers correspond to different time levels, and different time windows correspond to different time intervals, the linear combination of slow modes of each layer can form a multi-level, multi-frequency overall flow field reconstruction result. Therefore, the present invention can reconstruct the flow field of a gas-solid system based on existing gas-solid flow data samples using slow modes obtained from multi-resolution dynamic mode decomposition.

[0158] By employing the above method, this invention uses the slow modes retained in each decomposition layer as the basis for reconstruction, which helps to mitigate the problem of insufficient characterization of flow field changes within local time periods when relying solely on single-layer dynamic mode decomposition. Simultaneously, since the fast modes have already been recursively decomposed layer by layer in the aforementioned steps, and the corresponding slow modes are further extracted within finer time windows, the final reconstruction result can integrate slow mode information from different decomposition layers and different time windows. This is beneficial for improving the overall reconstruction result of the gas-solid system flow field's ability to characterize flow field changes at different time levels.

[0159] In one embodiment of the present invention, the gas-solid system multi-resolution dynamic mode decomposition and fast reconstruction method of the present invention further includes: The overall flow field reconstruction result is compared with the corresponding gas-solid flow result obtained by the CFD-DEM method, and the accuracy of the overall flow field reconstruction result is determined based on the comparison result. The comparison includes time-averaged physical field comparison and instantaneous physical field comparison. The time-averaged physical field includes at least one of the solids holdup time-averaged field, the mainstream velocity time-averaged field and the gas phase pressure time-averaged field. The instantaneous physical field includes at least one of the solids holdup instantaneous field, the solid phase velocity field along the mainstream direction and the solid phase volume flux field.

[0160] In one embodiment of the present invention, the corresponding gas-solid flow results obtained by the CFD-DEM method can be used as a comparison benchmark, and the overall flow field reconstruction result is the reconstruction result obtained based on the multi-resolution dynamic mode decomposition method. By comparing the distribution of the two under the same physical field, the same time conditions, or the same time-averaged statistical conditions, the reconstruction effect of the multi-resolution dynamic mode decomposition method on the flow field of the gas-solid two-phase flow system can be determined.

[0161] In one embodiment of the present invention, the comparison may include time-averaged physical field comparison and instantaneous physical field comparison. The time-averaged physical field comparison can be used to verify the ability of the method of the present invention to reconstruct the long-term or average flow characteristics of a gas-solid two-phase flow system, while the instantaneous physical field comparison can be used to verify the ability of the method of the present invention to reconstruct the transient flow structure at different times. In specific implementation, based on the gas-solid flow results obtained by the CFD-DEM method and the overall flow field reconstruction results obtained by the method of the present invention, the time-averaged field or instantaneous field corresponding to the same physical quantity can be extracted respectively, and the spatial distribution pattern, key feature structure, and overall change trend of the two can be compared to determine the accuracy of the overall flow field reconstruction results.

[0162] like Figure 9 As shown, in a specific embodiment of the present invention, the time-averaged fields of solids content, mainstream velocity, and gas phase pressure reconstructed by the multi-resolution dynamic mode decomposition method proposed in this invention can be compared with the corresponding time-averaged fields calculated by the CFD-DEM method. Figure 9It can be seen that for the time-averaged solids content, the CFD-DEM calculation results and the multi-resolution dynamic mode decomposition reconstruction results are basically consistent in overall distribution, both reflecting the solids content distribution characteristic of being sparser at the top and denser at the bottom along the height direction. For the time-averaged velocity in the mainstream direction, the CFD-DEM calculation results and the multi-resolution dynamic mode decomposition reconstruction results also have a relatively consistent distribution pattern, reflecting the phenomenon of higher velocity regions in the lower height and middle region of the bed. For the time-averaged gas phase pressure, the reconstruction results can well reflect the overall distribution of gas phase pressure along the height direction and the overall pressure drop characteristics. Therefore, it can be seen that in Figure 9 In the illustrated embodiment, the method of the present invention can reconstruct a variety of time-averaged physical fields in a gas-solid two-phase flow system with relatively high accuracy.

[0163] like Figure 10 As shown, in a specific embodiment of the present invention, the instantaneous fields reconstructed by the multi-resolution dynamic mode decomposition method proposed in this invention at different times can also be compared with the corresponding instantaneous fields calculated by the CFD-DEM method. Specifically, Figure 10 The instantaneous solid content field at t=0.300s, the solid velocity field along the mainstream direction at t=0.300s, the solid volume flux field at t=0.280s, and the solid volume flux field at t=0.015s are shown in comparison. Figure 10 It can be seen that for the instantaneous fields at different time points and with different physical quantities, the CFD-DEM calculation results and the multi-resolution dynamic mode decomposition reconstruction results have good consistency in terms of main distribution patterns and local structural features. This indicates that the method of the present invention can not only reconstruct the flow field features in the average sense, but also reconstruct the transient flow structure of the gas-solid two-phase flow system at different times.

[0164] pass Figure 9 The time-averaged physical field comparison shown and Figure 10 The instantaneous physical field comparison shown verifies that the multi-resolution dynamic mode decomposition method proposed in this invention can effectively reconstruct the flow field of a gas-solid two-phase flow system based on the linear combination of slow modes in each decomposition layer. Specifically, the comparison results of the time-averaged field show that the method of this invention can maintain the main average flow characteristics of the gas-solid system; the comparison results of the instantaneous field show that the method of this invention can reflect the transient distribution characteristics in the gas-solid flow field at different times. Therefore, the method of this invention can reconstruct the flow field of multiple physical fields in a gas-solid two-phase flow system based on existing gas-solid flow data samples, and can determine the accuracy of the reconstruction results by comparing them with the results of the CFD-DEM method.

[0165] It should be noted that, Figure 9 and Figure 10The time-averaged fields of solids holdup, velocity along the mainstream direction, gas pressure, instantaneous solids holdup, solid velocity along the mainstream direction, and solid volume flux shown are merely specific examples for verifying the accuracy of the overall flow field reconstruction results of this invention. In practical implementation, other physical quantities that can characterize the gas-solid flow state can also be used as comparison objects according to the analysis requirements of the gas-solid system to evaluate the overall flow field reconstruction results obtained by the method of this invention.

[0166] In an optional embodiment of the present invention, the comparison result can also be used to assist in determining the preset number of decomposition layers L in the layer-by-layer recursive dynamic modal decomposition process. Specifically, layer-by-layer recursive dynamic modal decomposition and flow field reconstruction can be performed first according to the initially set number of decomposition layers L, and the overall flow field reconstruction result obtained is compared with the corresponding gas-solid flow result obtained by the CFD-DEM method. If the comparison result shows that the current overall flow field reconstruction result does not meet the preset accuracy requirement, the number of decomposition layers L can be increased, and layer-by-layer recursive dynamic modal decomposition and flow field reconstruction can be performed again based on the increased number of decomposition layers; if the comparison result shows that the current overall flow field reconstruction result meets the preset accuracy requirement, the current number of decomposition layers L can be used as the number of decomposition layers used in this flow field reconstruction. In the above way, the selection of the number of decomposition layers L can be adjusted by using the comparison result between the overall flow field reconstruction result and the CFD-DEM method result, so that the recursive decomposition process can be adaptively set according to the reconstruction accuracy requirement, thereby ensuring the accuracy of flow field reconstruction while avoiding unnecessary increase in the number of decomposition layers and computational workload.

[0167] As can be seen from the above embodiments of the present invention, the gas-solid system multi-resolution dynamic mode decomposition and fast reconstruction method of the present invention achieves at least the following beneficial effects: 1. This invention utilizes the CFD-DEM method to generate gas-solid flow data samples of a gas-solid system at multiple time points. These gas-solid flow data samples include gas-solid flow information from each computational grid. Therefore, this invention can perform subsequent modal decomposition and flow field reconstruction based on relatively complete gas-solid flow field data. Compared to methods relying solely on local experimental measurement results, this approach is beneficial for more comprehensively characterizing the flow field distribution and its spatiotemporal variations within the gas-solid system.

[0168] 2. This invention performs multi-resolution dynamic modal decomposition based on gas-solid flow data samples. During the layer-by-layer recursive decomposition process, slow and fast modes are obtained for each decomposition layer. Even before the recursion termination condition is met, the fast modes are used as data samples for the next decomposition layer. Therefore, this invention can extract corresponding modal information within different decomposition layers and time windows, allowing for the stratified processing of slow-changing and faster-changing components in the gas-solid flow field. This improves the ability to characterize the complex spatiotemporal variations of gas-solid two-phase flow systems.

[0169] 3. This invention uses the slow modes retained within each decomposition layer and time window as the basis for flow field reconstruction. Flow field reconstruction terms are formed based on the modal amplitude, spatial mode, and temporal evolution term corresponding to each slow mode. These reconstructed terms are then linearly combined or superimposed to obtain the overall flow field reconstruction result of the gas-solid system. Therefore, this invention can achieve gas-solid flow field reconstruction based on existing gas-solid flow data samples, reducing the reliance on time-by-time processing of the entire flow field data during the reconstruction stage, and thus improving the processing efficiency of the gas-solid system flow field reconstruction process.

[0170] 4. By retaining the slow modes of each decomposition layer and continuing to decompose the fast modes before the recursion termination condition is met, this invention can further extract effective modal information that can be used for reconstruction from the faster-changing components corresponding to the fast modes. Therefore, compared to performing single-layer dynamic modal decomposition on only the complete time series, this invention can form a multi-level, multi-time-window reconstruction structure, which is beneficial for improving the characterization effect of the reconstruction results on flow field changes and non-uniform flow structures such as particle agglomeration and bubbles within local time periods.

[0171] 5. This invention can compare the overall flow field reconstruction results obtained from multi-resolution dynamic mode decomposition with the corresponding gas-solid flow results obtained by the CFD-DEM method, and determine the accuracy of the reconstruction results by comparing the time-averaged physical field and the instantaneous physical field. Specific embodiments show that the method of this invention can reconstruct the time-averaged field of solid holdup, the time-averaged field of velocity along the mainstream direction, the time-averaged field of gas phase pressure, as well as the instantaneous field of solid holdup, the velocity field of the solid phase along the mainstream direction, and the volume flux field of the solid phase at different time points, thereby verifying the effectiveness of the method of this invention for flow field reconstruction of gas-solid two-phase flow systems.

[0172] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0173] Based on the same inventive concept, embodiments of the present invention also provide a device for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems, which can be used to implement the gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction method described in the above embodiments, as described in the following embodiments. Since the principle of the gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction device is similar to that of the gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction method, embodiments of the gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction device can refer to embodiments of the gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction method, and repeated details will not be elaborated further. As used below, the terms "unit" or "module" can refer to a combination of software and / or hardware that implements a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0174] Figure 11 This is a structural block diagram of the gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction device according to an embodiment of the present invention, as shown below. Figure 11 As shown, in one embodiment of the present invention, the gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction device of the present invention includes: Sample forming unit 1 is used to form gas-solid flow data samples of a gas-solid system at multiple time points using the CFD-DEM method. The gas-solid flow data samples include gas-solid flow information of each computation grid. The decomposition and reconstruction unit 2 is used to perform multi-resolution dynamic mode decomposition based on the gas-solid flow data samples. During the layer-by-layer recursive decomposition process, the data samples to be decomposed in the current decomposition layer are decomposed to obtain the slow mode and fast mode of the current decomposition layer. The slow mode of the current decomposition layer is retained for subsequent flow field reconstruction. If the recursion termination condition is not met, the data samples to be decomposed in the next decomposition layer are formed based on the fast mode of the current decomposition layer to continue the mode decomposition of the next decomposition layer until the slow mode and fast mode of each decomposition layer are obtained. The flow field of the gas-solid system is reconstructed based on the slow mode of each decomposition layer to obtain the overall flow field reconstruction result of the gas-solid system.

[0175] In one embodiment of the present invention, the decomposition and reconstruction unit includes: The first-layer decomposition module is used to construct a first snapshot matrix and a second snapshot matrix with adjacent time misalignment based on the gas-solid flow data sample, and to perform dynamic mode decomposition based on the first snapshot matrix and the second snapshot matrix to obtain the first-layer slow mode and the first-layer fast mode. The recursive decomposition module is used to perform layer-by-layer recursive dynamic mode decomposition using the first-layer fast mode as the initial data sample to be decomposed. In the process of layer-by-layer recursive dynamic mode decomposition, for each data sample to be decomposed in the current decomposition layer, the data sample to be decomposed is divided into two sub-data samples according to the time window, and dynamic mode decomposition is performed on each sub-data sample to obtain the slow mode and fast mode of the current layer corresponding to each sub-data sample. Each fast mode of the current layer is used as the data sample to be decomposed in the next decomposition layer. The flow field reconstruction module is used to combine the slow modes of each layer to obtain the overall flow field reconstruction result of the gas-solid system.

[0176] In one embodiment of the present invention, the plurality of times are M sampling times arranged consecutively according to a preset unit time step; The first-level decomposition module includes: The snapshot vector generation submodule is used to arrange the gas-solid flow information of each computational grid at each sampling time into the corresponding flow field snapshot vector according to the same grid order; The snapshot matrix construction submodule is used to form the first snapshot matrix by combining the flow field snapshot vectors corresponding to the first sampling time to the (M-1)th sampling time in chronological order, and to form the second snapshot matrix by combining the flow field snapshot vectors corresponding to the second sampling time to the Mth sampling time.

[0177] In one embodiment of the present invention, the first-layer decomposition module includes: The singular value decomposition submodule is used to perform singular value decomposition on the first snapshot matrix to obtain the POD mode matrix, the singular value matrix and the right singular vector matrix. The projection matrix determination submodule is used to determine the projection matrix of the operator matrix representing the linear mapping relationship between the first snapshot matrix and the second snapshot matrix in the POD modality space based on the conjugate transpose of the POD modality matrix, the second snapshot matrix, the right singular vector matrix, and the inverse matrix of the singular value matrix. The projection matrix decomposition submodule is used to perform eigenvalue decomposition on the projection matrix to obtain the eigenvector matrix and the eigenvalue diagonal matrix of the projection matrix; The operator decomposition submodule is used to determine the eigenvector matrix of the operator matrix based on the eigenvector matrix of the projection matrix, and in combination with the inverse matrix of the second snapshot matrix, the right singular vector matrix, and the singular value matrix, and to determine the eigenvalue diagonal matrix of the operator matrix based on the eigenvalue diagonal matrix of the projection matrix, thereby obtaining the eigenvalue decomposition of the operator matrix. The modality partitioning submodule is used to obtain a dynamic modality decomposition expression based on the eigenvalue decomposition of the operator matrix, and to divide the modes in the dynamic modality decomposition expression into a slow modality part and a fast modality part according to a preset modality partitioning method. The slow modality part is determined as the first layer of slow modes, and the fast modality part is determined as the first layer of fast modes.

[0178] In one embodiment of the present invention, the recursive decomposition module includes: The second-layer decomposition submodule is used to take the first-layer fast mode as the data sample to be decomposed in the second layer, divide the data sample to be decomposed in the second layer into two second-layer sub-data samples according to the time window, and perform dynamic mode decomposition on the two second-layer sub-data samples respectively to obtain the second-layer slow mode and the second-layer fast mode corresponding to each of the two second-layer sub-data samples. The second-layer slow mode corresponding to each of the two second-layer sub-data samples is retained for subsequent flow field reconstruction. If the recursion termination condition is not reached, the second-layer fast mode corresponding to each of the two second-layer sub-data samples is used as the data sample to be decomposed in the third layer. In the subsequent layer decomposition submodule, for the third layer and subsequent layers, for each data sample to be decomposed in the current layer, the data sample to be decomposed is divided into two current layer sub-data samples according to the time window, and dynamic mode decomposition is performed on each current layer sub-data sample to obtain the current layer slow mode and the current layer fast mode corresponding to each current layer sub-data sample. The current layer slow mode corresponding to each current layer sub-data sample is retained for subsequent flow field reconstruction, and if the recursion termination condition is not reached, the current layer fast mode corresponding to each current layer sub-data sample is used as the data sample to be decomposed in the next layer.

[0179] In one embodiment of the present invention, the flow field reconstruction module includes: The reconstruction term forms a sub-module, which is used to form a corresponding flow field reconstruction term for each slow mode in each layer and time window, based on the modal amplitude, spatial mode and temporal evolution term corresponding to the slow mode; The reconstruction item superposition submodule is used to superimpose the flow field reconstruction items to obtain the overall flow field reconstruction result of the gas-solid system.

[0180] In one embodiment of the present invention, the gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction device of the present invention further includes: An accuracy determination unit is used to compare the overall flow field reconstruction result with the corresponding gas-solid flow result obtained by the CFD-DEM method, and determine the accuracy of the overall flow field reconstruction result based on the comparison result. The comparison includes time-averaged physical field comparison and instantaneous physical field comparison. The time-averaged physical field includes at least one of the solids holdup time-averaged field, the mainstream velocity time-averaged field, and the gas phase pressure time-averaged field. The instantaneous physical field includes at least one of the solids holdup instantaneous field, the solid phase velocity field along the mainstream direction, and the solid phase volume flux field.

[0181] To achieve the above objectives, according to another aspect of this application, a computer device is also provided. For example... Figure 12 As shown, the computer device includes a memory, a processor, a communication interface, and a communication bus. The memory stores a computer program that can run on the processor. When the processor executes the computer program, it implements the steps in the method of the above embodiments.

[0182] The processor can be a central processing unit (CPU). The processor can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or combinations of the above types of chips.

[0183] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and units, such as the program units corresponding to the above-described method embodiments of the present invention. The processor executes various functional applications and data processing of the processor by running the non-transitory software programs, instructions, and modules stored in the memory, thereby implementing the methods described in the above-described method embodiments.

[0184] The memory may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created by the processor, etc. Furthermore, the memory may include high-speed random access memory and non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory may optionally include memory remotely located relative to the processor, which can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0185] The one or more units are stored in the memory and, when executed by the processor, perform the methods described in the above embodiments.

[0186] The specific details of the aforementioned computer equipment can be understood by referring to the relevant descriptions and effects in the above embodiments, and will not be repeated here.

[0187] To achieve the above objectives, according to another aspect of this application, a computer-readable storage medium is also provided, which stores a computer program that, when executed in a computer processor, implements the steps in the above-described method for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems. Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), etc.; the storage medium may also include combinations of the above types of memory.

[0188] To achieve the above objectives, according to another aspect of this application, a computer program product is also provided, including a computer program / instructions that, when executed by a processor, implement the steps of the above-described gas-solid system multi-resolution dynamic mode decomposition and rapid reconstruction method.

[0189] Obviously, those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device, or fabricating them separately as individual integrated circuit modules, or fabricating multiple modules or steps as a single integrated circuit module. Thus, the present invention is not limited to any particular hardware and software combination.

[0190] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for multi-resolution dynamic mode decomposition and fast reconstruction of a gas-solid system, characterized in that, include: The CFD-DEM method is used to generate gas-solid flow data samples of a gas-solid system at multiple time points. The gas-solid flow data samples include gas-solid flow information of each computation grid. Multi-resolution dynamic mode decomposition is performed based on the gas-solid flow data samples. During the layer-by-layer recursive decomposition process, mode decomposition is performed on the data samples to be decomposed in the current decomposition layer to obtain the slow mode and fast mode of the current decomposition layer. The slow mode of the current decomposition layer is retained for subsequent flow field reconstruction. If the recursion termination condition is not met, the data samples to be decomposed in the next decomposition layer are formed based on the fast mode of the current decomposition layer to continue the mode decomposition of the next decomposition layer until the slow mode and fast mode of each decomposition layer are obtained. The flow field of the gas-solid system is reconstructed based on the slow mode of each decomposition layer to obtain the overall flow field reconstruction result of the gas-solid system.

2. The method for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems according to claim 1, characterized in that, The process of performing multi-resolution dynamic mode decomposition based on the gas-solid flow data samples involves recursively decomposing the data samples to be decomposed at the current decomposition layer to obtain the slow and fast modes of the current decomposition layer. The slow modes of the current decomposition layer are retained for subsequent flow field reconstruction. If the recursion termination condition is not met, the data samples to be decomposed at the next decomposition layer are generated based on the fast modes of the current decomposition layer to continue the mode decomposition at the next decomposition layer, until the slow and fast modes of each decomposition layer are obtained. The flow field of the gas-solid system is reconstructed based on the slow modes of each decomposition layer to obtain the overall reconstructed flow field result of the gas-solid system, including: Based on the gas-solid flow data samples, a first snapshot matrix and a second snapshot matrix with a misalignment relationship between adjacent time moments are constructed, and dynamic mode decomposition is performed based on the first snapshot matrix and the second snapshot matrix to obtain the first slow mode and the first fast mode. The first fast mode is used as the initial data sample to be decomposed and recursively dynamic mode decomposition is performed layer by layer. In the process of recursively dynamic mode decomposition, for each data sample to be decomposed in the current decomposition layer, the data sample to be decomposed is divided into two sub-data samples according to the time window, and dynamic mode decomposition is performed on each sub-data sample to obtain the slow mode and fast mode of the current layer corresponding to each sub-data sample. Each fast mode of the current layer is used as the data sample to be decomposed in the next decomposition layer. By combining the slow modes of each layer, the overall flow field reconstruction result of the gas-solid system is obtained.

3. The method for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems according to claim 2, characterized in that, The multiple time points are M sampling time points arranged consecutively according to a preset unit time step; The construction of a first snapshot matrix and a second snapshot matrix with a misalignment relationship between adjacent time points based on the gas-solid flow data samples includes: The gas-solid flow information of each computational grid at each sampling time is arranged in the same grid order to form the corresponding flow field snapshot vector; In chronological order, the flow field snapshot vectors corresponding to the first sampling time to the (M-1)th sampling time are used to form the first snapshot matrix, and the flow field snapshot vectors corresponding to the second sampling time to the Mth sampling time are used to form the second snapshot matrix.

4. The method for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems according to claim 2, characterized in that, The dynamic mode decomposition based on the first snapshot matrix and the second snapshot matrix to obtain the first layer of slow modes and the first layer of fast modes includes: Singular value decomposition is performed on the first snapshot matrix to obtain the POD mode matrix, singular value matrix, and right singular vector matrix; Based on the conjugate transpose of the POD modality matrix, the second snapshot matrix, the right singular vector matrix, and the inverse of the singular value matrix, determine the projection matrix of the operator matrix representing the linear mapping relationship between the first snapshot matrix and the second snapshot matrix in the POD modality space; The projection matrix is ​​subjected to eigenvalue decomposition to obtain the eigenvector matrix and the eigenvalue diagonal matrix of the projection matrix; Based on the eigenvector matrix of the projection matrix, and combined with the inverse matrices of the second snapshot matrix, the right singular vector matrix, and the singular value matrix, the eigenvector matrix of the operator matrix is ​​determined, and the eigenvalue diagonal matrix of the operator matrix is ​​determined based on the eigenvalue diagonal matrix of the projection matrix, thereby obtaining the eigenvalue decomposition of the operator matrix. The dynamic mode decomposition expression is obtained based on the eigenvalue decomposition of the operator matrix. According to the preset mode partitioning method, the modes in the dynamic mode decomposition expression are divided into slow mode parts and fast mode parts. The slow mode parts are determined as the first layer of slow modes, and the fast mode parts are determined as the first layer of fast modes.

5. The method for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems according to claim 2, characterized in that, The step involves using the first-layer fast mode as the initial data sample to be decomposed and performing layer-by-layer recursive dynamic mode decomposition. During this process, for each data sample to be decomposed in the current decomposition layer, the data sample is divided into two sub-data samples according to a time window. Dynamic mode decomposition is then performed on each sub-data sample to obtain the slow mode and fast mode corresponding to each sub-data sample in the current layer. Each fast mode in the current layer is then used as the data sample to be decomposed in the next decomposition layer. This includes: The first fast mode is used as the data sample to be decomposed in the second layer. The data sample to be decomposed in the second layer is divided into two sub-data samples of the second layer according to the time window. Dynamic mode decomposition is performed on the two sub-data samples of the second layer respectively to obtain the second slow mode and the second fast mode corresponding to each of the two sub-data samples of the second layer. The second slow mode corresponding to each of the two sub-data samples of the second layer is retained for subsequent flow field reconstruction. If the recursion termination condition is not met, the second fast mode corresponding to each of the two sub-data samples of the second layer is used as the data sample to be decomposed in the third layer. For the third layer and subsequent layers, for each data sample to be decomposed in the current layer, the data sample to be decomposed is divided into two current layer sub-data samples according to the time window, and dynamic mode decomposition is performed on each current layer sub-data sample to obtain the current layer slow mode and the current layer fast mode corresponding to each current layer sub-data sample. The current layer slow mode corresponding to each current layer sub-data sample is retained for subsequent flow field reconstruction, and if the recursion termination condition is not met, the current layer fast mode corresponding to each current layer sub-data sample is used as the data sample to be decomposed in the next layer.

6. The method for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems according to claim 2, characterized in that, The combined slow modes of each layer are used to obtain the overall reconstructed flow field of the gas-solid system, including: For each slow mode within each time window of each layer, a corresponding flow field reconstruction term is formed based on the modal amplitude, spatial mode, and temporal evolution term corresponding to the slow mode; The flow field reconstruction terms are superimposed to obtain the overall flow field reconstruction result of the gas-solid system.

7. The method for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems according to claim 1, characterized in that, Also includes: The overall flow field reconstruction result is compared with the corresponding gas-solid flow result obtained by the CFD-DEM method, and the accuracy of the overall flow field reconstruction result is determined based on the comparison result. The comparison includes time-averaged physical field comparison and instantaneous physical field comparison. The time-averaged physical field includes at least one of the solids holdup time-averaged field, the mainstream velocity time-averaged field and the gas phase pressure time-averaged field. The instantaneous physical field includes at least one of the solids holdup instantaneous field, the solid phase velocity field along the mainstream direction and the solid phase volume flux field.

8. The method for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems according to claim 1, characterized in that, The gas-solid flow information includes at least one of solid holdup, average solid velocity, average gas velocity, gas pressure, and solid volumetric flux.

9. The method for multi-resolution dynamic mode decomposition and rapid reconstruction of gas-solid systems according to claim 1, characterized in that, The CFD-DEM method employs an Eulerian-Lagrange method with local mesh refinement for simulation. During the simulation, the Eulerian method is used to solve for gas phase motion characteristics, while the Lagrange method is used to solve for particle motion characteristics. The Eulerian-Lagrange method is coupled using a normalized kernel function method and a particle center-of-mass method, and the normalized kernel function is used to achieve data mapping between the Eulerian-described gas phase computational mesh and the Lagrange-described particle mesh.

10. A device for multi-resolution dynamic mode decomposition and rapid reconstruction of a gas-solid system, characterized in that, include: The sample forming unit is used to form gas-solid flow data samples of the gas-solid system at multiple time points using the CFD-DEM method. The gas-solid flow data samples include gas-solid flow information of each computation grid. The decomposition and reconstruction unit is used to perform multi-resolution dynamic mode decomposition based on the gas-solid flow data samples. During the layer-by-layer recursive decomposition process, the data samples to be decomposed in the current decomposition layer are decomposed to obtain the slow mode and fast mode of the current decomposition layer. The slow mode of the current decomposition layer is retained for subsequent flow field reconstruction. If the recursion termination condition is not met, the data samples to be decomposed in the next decomposition layer are formed based on the fast mode of the current decomposition layer to continue the mode decomposition of the next decomposition layer until the slow mode and fast mode of each decomposition layer are obtained. The flow field of the gas-solid system is reconstructed based on the slow mode of each decomposition layer to obtain the overall flow field reconstruction result of the gas-solid system.

11. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 9.

12. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 9.

13. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 9.

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