Multiphase flow flow control and heat exchange simulation system

Abstract

The invention relates to the technical field of computational fluid mechanics and system control, and discloses a multiphase flow flow control and heat exchange simulation system, which comprises a multi-physical field tensor modeling module for reconstructing a control equation into a uniform high-order tensor and extracting a curvature tensor; the dynamic tensor dimension reduction and implicit coupling solving module is used for performing dynamic rank reduction on the tensor equation and constructing a tensor product Jacobian matrix; the physical constraint agent modeling and migration optimization module is used for constructing an agent objective function embedded with a physical conservation law; the asynchronous time stepping and multi-scale coordination module is used for realizing asynchronous time propulsion and strong coupling solution based on curvature tensor; and the multi-objective optimization and decision mapping module is used for performing multi-objective optimization based on the proxy objective function. According to the method, a multi-physical field control equation is reconstructed into a unified high-order tensor, and a tensor decomposition strategy for dynamic rank adaptive adjustment based on a phase interface curvature tensor and a Jacobian condition number is combined, so that efficient and stable solution of the high-dimensional coupling physical system is realized.

Description

Technical Field

[0001] The present invention relates to the field of computational fluid dynamics and system control technology, and in particular to a multiphase flow control and heat exchange simulation system. Background Art

[0002] Multiphase flow and heat transfer phenomena are ubiquitous in modern industry and cutting-edge science, and their efficient regulation and precise prediction are key to technological innovation. For example, in nuclear reactors, the boiling and flow of coolant are directly related to core safety; in chemical processes, the mixing efficiency of gas-liquid reactors determines product yield and energy consumption; and in aircraft engines, the atomization and combustion of fuel influence thrust performance and emissions.

[0003] Numerical simulation technology for multiphase flows has made significant progress. Leveraging high-performance computing platforms, existing computational fluid dynamics (CFD) methods enable detailed analysis of physical processes under specific operating conditions. These techniques, under given boundary conditions and physical parameters, provide high-resolution distribution information of flow fields, temperature fields, and phase interfaces. Through in-depth analysis of specific scenarios, these technologies provide powerful support for understanding complex flow and heat transfer mechanisms, validating experimental data, and diagnosing localized problems, playing a vital role in engineering analysis and scientific research.

[0004] However, the existing technology still faces several deep-seated bottlenecks when dealing with the coupled solution and optimization control of complex systems, which are precisely the problems that the present invention is committed to solving. First, when trying to solve the strong coupling of multiple physical fields, the existing model will generate a set of algebraic equations with extremely high dimensions and poor properties, resulting in a sharp increase in computational cost with the scale of the problem, making it impractical to perform high-fidelity, fully coupled simulations of large-scale systems. Secondly, when performing optimization design, if traditional simulation is directly used as an evaluation tool, its huge single-time calculation time makes the optimization process extremely long. If a pure data-driven proxy model lacking physical connotation is used, the physical authenticity of its output results cannot be guaranteed, and its optimization suggestions will violate basic conservation laws. Finally, the existing simulation framework generally adopts a globally unified time step, which is limited by the fastest and smallest local phenomena in the system, resulting in a huge waste of computing resources in a large area with gentle changes, greatly limiting the simulation efficiency of long-term evolution processes. To this end, those skilled in the art have proposed a multiphase flow control and heat transfer simulation system to solve the above problems. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the present invention provides a multiphase flow control and heat exchange simulation system, which solves technical problems in the existing technology, such as the contradiction between solution efficiency and physical accuracy of simulation models, the difficulty of multi-objective optimization in balancing speed and physical reality, and the rigid allocation of computing resources in time and space scales.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solutions: A multiphase flow control and heat exchange simulation system, comprising: A multi-physics tensor modeling module is used to reconstruct the control equations in a unified high-order tensor form based on the preset scalar or vector form of the control equations describing multiphase flow, heat transfer and phase field, and to extract the phase interface curvature tensor from the phase field control equations in the high-order tensor form; a dynamic tensor dimensionality reduction and implicit coupling solution module, configured to receive the control equations in the form of high-order tensors and the phase interface curvature tensor, perform dynamic rank dimensionality reduction on the control equations in the form of high-order tensors, and construct a Jacobian matrix in the form of a tensor product that matches the rank of the dimensionality reduction; A physical constraint agent modeling and migration optimization module for constructing an agent objective function embedded with physical conservation laws based on the control equations in the form of high-order tensors; an asynchronous time stepping and multi-scale coordination module for asynchronously advancing the flow field and the heat transfer field using different time steps based on the phase interface curvature tensor, and performing an implicit strong-coupling solution to the dimensionality-reduced governing equations using the Jacobian matrix in the form of the tensor product; The multi-objective optimization and decision mapping module is used to perform multi-objective optimization based on the results of the proxy objective function and the implicit strong coupling solution, and map the optimization results back to the original control parameter space.

[0007] Preferably, the multi-physics field tensor modeling module includes: Obtaining a plurality of control equations for describing the evolution of the velocity field, the temperature field, and the phase field, and extracting control variables from the control equations; According to the spatiotemporal distribution dimensions of the control variables, a unified high-order tensor expression is constructed so that the control variables can be stored in a fourth-order tensor structure. The phase interface normal vector is calculated from the phase field tensor, and then the phase interface curvature tensor is calculated based on the vector, and the tensor is used as an indicator input for subsequent rank reduction and time step control.

[0008] Preferably, the phase interface curvature tensor calculation process includes: The interface normal distribution is calculated by combining the gradient and the normalized direction vector; The interface curvature tensor is obtained by calculating the second-order derivative of the normal vector tensor field; The curvature tensor is normed and time-domain smoothed for dynamic time step adjustment.

[0009] Preferably, the dynamic tensor dimensionality reduction and implicit coupling solution module includes: Determining the optimal decomposition rank of the high-order tensor expression based on the norm of the phase interface curvature tensor and the condition number of the current Jacobian matrix; Performing low-rank reconstruction on the high-order tensor expression using a tensor decomposition algorithm and generating a dimensionality-reduced tensor model; A Jacobian matrix in tensor product form matching the decomposition rank is constructed, and the Jacobian matrix is used in a subsequent iterative structure solving process.

[0010] Preferably, the tensor decomposition algorithm is a Tucker decomposition algorithm with rank adaptive adjustment, and the algorithm includes: Initialize multiple tensor kernels and factor matrices, and set rank upper bounds and error thresholds; Dynamically adjust the decomposition rank according to the control tensor residual during each dimensionality reduction process; The iteration termination condition is determined based on the reconstruction error between the decomposed tensor and the original tensor.

[0011] Preferably, the physical constraint agent modeling and migration optimization module includes: Construct a set of basis functions for expressing tensor control relationships and perform physical consistency training on the basis function set to ensure that the basis function set satisfies the preset conservation law conditions; A proxy objective function is constructed based on a linear combination of multiple basis functions, and this proxy objective function is embedded into the tensor control framework as a proxy model that can quickly predict system performance. A conservation error term is set and a Lagrange multiplier is introduced, and the residual is embedded into the objective function as an additional constraint for subsequent optimization solution.

[0012] Preferably, the process of constructing the proxy objective function includes: The surrogate function is trained with weak form integral residuals in multiple known sample scenarios; The time derivative of the field variable is introduced to construct the deviation term with the physical operator term in the tensor control equation; Control the residuals on all basis functions to not exceed a preset physical tolerance threshold.

[0013] Preferably, the asynchronous time stepping and multi-scale coordination module includes: Determine the local time step of the flow field based on the current flow field velocity distribution and the computational domain spatial step; Calculate the norm of the interface curvature tensor and adjust the time step of the heat transfer field based on this value to achieve dynamic matching of time scales between different physical fields; Independent time steps are used for the control equations corresponding to different control variables, and tensor increments are solved simultaneously in each step.

[0014] Preferably, the multi-objective optimization and decision mapping module includes: Setting a plurality of performance objective functions for measuring simulation results, and uniformly embedding the objective functions into the agent model; Under the condition of maintaining physical conservation constraints, a multi-objective optimization algorithm is used to search for a non-inferior solution set in the control parameter space. The non-inferior solution set consists of a set of optimal solutions that cannot be replaced by each other, and each optimal solution corresponds to a set of input control parameters, forming a non-inferior solution control parameter group; The non-inferior solution control parameter group is mapped to the original control parameter space in the space of the proxy model, and a constraint consistency check is performed.

[0015] Preferably, the multi-objective optimization algorithm adopts an evolutionary multi-objective optimization method based on Pareto frontier search, including: Construct a joint evaluation index of the objective function value and the residual constraint term based on the output results of the surrogate model; Perform Pareto sorting on the search results and screen the frontier of non-inferior solutions; The non-inferior solution control parameter group is input into the simulation system for re-calibration to determine the optimal mapping result.

[0016] The present invention provides a multiphase flow control and heat exchange simulation system. It has the following beneficial effects: 1. The present invention reconstructs the multi-physics field control equations into a unified high-order tensor, and combines it with a tensor decomposition strategy based on the phase interface curvature tensor and the Jacobian condition number for dynamic rank adaptive adjustment, thereby achieving efficient and stable solution of high-dimensional coupled physical systems. Compared with the existing technology that uses separable solvers or fixed full-order models to deal with multiphase flow problems, the present invention solves the technical bottlenecks of the surge in computational costs caused by the high model dimension and the easy occurrence of numerical oscillations or convergence difficulties in the strong coupling region.

[0017] 2. The present invention significantly improves the convergence speed of the multi-objective optimization process and the physical reliability of the results by constructing a proxy objective function embedded with physical conservation laws and introducing the weak form integral residual of the control equation into the optimization framework as a Lagrange multiplier constraint term. This solution is different from the existing technology that relies on full-scale simulation for iterative optimization or adopts a purely data-driven proxy model. It effectively solves the inherent defects of the former, which leads to low optimization efficiency due to the high cost of a single evaluation, and the latter, which produces pseudo-optimal solutions or violates conservation laws due to the lack of physical constraints.

[0018] 3. The asynchronous time stepping and multi-scale coordination scheme adopted by the present invention utilizes the phase interface curvature tensor to dynamically control the time advancement scale of different physical fields, and combines the Jacobian matrix in the form of tensor product for strong coupling solution, thereby realizing the intelligent allocation of computing resources in the time domain and the physical domain, and greatly shortening the simulation cycle while ensuring the accuracy of analysis in key areas. Compared with the existing technology that generally adopts the strategy of synchronous advancement with a global unified minimum time step, the present invention overcomes the deficiency of low global computing efficiency caused by meeting the most stringent local stability conditions, and solves the problem of serious waste of computing resources when multi-scale physical phenomena coexist. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the system architecture of the present invention; Figure 2 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0020] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the present specification. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0021] Please see the attached Figure 1 and attached Figure 2 The embodiment of the present invention provides a multiphase flow control and heat transfer simulation system, comprising: The multi-physics tensor modeling module is used to reconstruct the governing equations of multiphase flow, heat transfer, and phase field into a unified high-order tensor form based on the preset scalar or vector form of the governing equations, and to extract the phase interface curvature tensor from the high-order tensor form of the phase field governing equations; Specifically, in the multiphase flow control and heat transfer simulation system provided by the present invention, the system structure has a clear hierarchical division, and the modules are logically connected through tensor control equations and their characteristic quantities. Among them, the multi-physics field tensor modeling module, as the first core unit of the system, not only provides a unified, high-dimensional control expression foundation for subsequent modules, but also directly supports the entire process of dimensionality reduction analysis, time step coordination, and objective function construction by extracting key tensor quantitative information such as phase interface curvature.

[0022] Existing multiphase flow modeling methods typically rely on several independent governing equations to describe the conservation of momentum, energy, and mass, as well as the evolution of the phase field. However, these methods suffer from inconsistent expression structures, inconsistent control variable dimensions, and difficulty in data fusion when addressing high-dimensional coupling problems, making them difficult to meet the demands of subsequent coupling solutions and optimization control.

[0023] To overcome these issues, this paper proposes a unified tensor modeling strategy for multiple physical fields. By reconstructing the governing equations into tensors, unified modeling across physical domains is achieved. In one possible implementation, the tensor control structure uses fourth-order tensors to represent the variables and their derivatives in the governing equations, organizing and storing them uniformly in a joint time-space-variable tensor space.

[0024] In this embodiment, the multi-physics tensor modeling module first obtains the governing equations for describing the multiphase flow system, including but not limited to: Momentum conservation equation: ; Energy equation: ; Phase field evolution equations (such as the Cahn-Hilliard equation): ; in: Indicates density; Indicates the The velocity components in each direction; Indicates pressure; represents the stress tensor; represents the body force term; represents enthalpy; Indicates temperature; Indicates time; represents thermal conductivity; Indicates body heat source; represents the phase field function; represents chemical potential; represents the migration rate; Indicates the Partial derivatives in spatial dimensions; Indicates the Partial derivatives in spatial dimensions.

[0025] As an option, for each control quantity in the above equation in the spatial dimension , time dimension , physical variable dimension The distribution on it constructs a unified tensor control structure of the following form: ; in: represents the tensor coefficient of the time derivative of the control variable; represents the flux term related tensor; represents the source term tensor; For the A control variable, which can be expressed as a velocity component ,temperature , or phase field ; For the A control variable, which can be expressed as a velocity component ,temperature , or phase field ; The four subscripts of the tensor represent the joint mapping of the time dimension, the three spatial dimensions, and the physical variable dimension.

[0026] In some embodiments, to facilitate subsequent time step control and dimensionality reduction rank adjustment processing, the module further extracts the interface curvature tensor from the phase field tensor control equation The process includes the following steps: Specifically, first the phase field function Perform gradient operations on the spatial dimension to obtain the normal vector tensor field: ; in: is the unit normal vector at the interface Directional component; is the gradient norm of the phase field function; is the phase field function for the Partial derivatives with respect to spatial coordinates.

[0027] Then, the interface curvature tensor is calculated based on the normal vector tensor field: ; in: Normal vector Quantity Partial derivatives with respect to spatial coordinates.

[0028] As a possible implementation method, in order to ensure numerical stability, after the curvature tensor is extracted, further tensor norm processing and time domain sliding average operation can be performed: ; ; in: is a tensor The Frobenius norm of For all spatial dimensions The index is summed; For the current time At Sliding time average of the components; is the sliding window time scale; is the integral variable, representing time.

[0029] In one implementation, the unified tensor control expression and its interface feature tensor are cached in a structured data unit and serve as the standard input format for the tensor dimensionality reduction and implicit solver modules. Furthermore, to support heterogeneous field coupling, the module allows multiple control equations to coexist and be uniformly mapped into a high-order tensor space, independent of their specific form.

[0030] It is worth noting that the tensor modeling strategy supports extension to higher-order tensor fields, and is applicable to six-dimensional phase space modeling, three-phase interface problems, and multi-property discontinuous control problems, providing a general expression structure for subsequent processing.

[0031] In actual implementation, the tensor expression layer of this module is implemented based on a sparse structure and supports parallel tensor operations for the GPU architecture, ensuring computational efficiency and scalability in large-scale grid structures.

[0032] Dynamic tensor dimensionality reduction and implicit coupling solution module, which is used to receive the control equations and phase interface curvature tensor in high-order tensor form, dynamically reduce the rank of the control equations in high-order tensor form, and construct a Jacobian matrix in tensor product form that matches the rank of the reduced dimensionality; Specifically, after the aforementioned modules complete the construction of the unified tensor governing equations for multiple physical fields, to meet the computational complexity control requirements in large-scale coupled solutions, the present invention further structurally introduces a dynamic tensor dimensionality reduction and implicit coupling solution module. This module takes the tensorized governing equations and the phase interface characteristic tensor as input, and develops around tensor rank compression and tensor Jacobian matrix construction, aiming to reduce the solution dimensionality while ensuring the accuracy of tensor expression, and establish a solver interface that matches the dimensionality reduction structure.

[0033] Generally speaking, for fourth-order or higher-order tensor control structures, the solution efficiency in numerical simulations is often significantly reduced due to the curse of dimensionality. In particular, when strong correlations between coupled fields are involved, the lack of effective low-rank modeling methods will make it impossible to balance accuracy and solution cost. The module of the present invention combines the dynamic evolution characteristics of the phase interface structure tensor to construct an adaptive rank adjustment mechanism, and supplemented by a tensor decomposition algorithm and a tensor product structure Jacobian construction strategy, to achieve the generation and solution of low-rank structural models that are highly coordinated with the control equations.

[0034] In this embodiment, the dynamic tensor dimensionality reduction and implicit coupling solution module receives input from the multi-physics field tensor modeling module, mainly including the unified tensor control equation of the previous module and the phase interface curvature tensor of the previous module.

[0035] In one possible implementation, the module first determines the optimal decomposition rank of the current tensor system based on the Frobenius norm of the phase interface curvature tensor and the condition number of the Jacobian matrix in the current iteration. The process follows the following expression: ; in: represents the target tensor rank; is the adjustment factor, and its value range is ; represents the Frobenius norm of the curvature tensor; Indicates the condition number of the currently constructed Jacobian matrix; Represents the ceiling function.

[0036] As an option, this module supports multiple tensor decomposition strategies, including but not limited to CANDECOMP / PARAFAC decomposition (CP decomposition) and Tucker decomposition. In this embodiment, Tucker decomposition with rank adaptation is adopted. The specific steps include: Initialize Tensor Cores And the factor matrix of each dimension ,in For the The tensor size of dimension, is the target rank for this dimension.

[0037] In each dimensionality reduction step, the residual is reconstructed from a tensor: ; Error tolerance , dynamically adjust the rank values of each dimension until it satisfies: ; in: Represents the first Modulus; represents the Frobenius norm; Generally set in within the range.

[0038] Specifically, the tensor control expression is expressed in a compact form after dimensionality reduction, providing a rank constraint basis for the subsequent Jacobian matrix construction. After the dimensionality reduction is completed, this module further constructs a tensor product Jacobian matrix that matches the reduced rank structure: ; in: represents the global Jacobian matrix; For the The component Jacobians in the directions; represents the Kronecker product symbol; Decompose the rank of the current tensor.

[0039] In some embodiments, the Kronecker construction process can be combined with Jacobi block preconditioning technology to perform partitioned sparse optimization, thereby effectively reducing matrix storage and computational overhead while maintaining a strongly coupled structure.

[0040] As an implementation strategy, this module generates a reduced-dimensional tensor control system and its tensor product structure Jacobian matrix, which is exported as a structured interface for the subsequent coupled solution of the implicit time advancer and the construction of the proxy objective function. Notably, this module supports dynamic rank re-evaluation and tensor structure updates within each time step to accommodate interface changes or increased dimensionality in high-gradient regions.

[0041] In actual deployment, the module also supports caching the reduced-dimensional structure to the GPU tensor computing unit, further improving the solution efficiency through parallel tensor-matrix core operations, and is suitable for high-fidelity simulation tasks in ultra-large-scale control spaces.

[0042] Physical Constraint Agent Modeling and Transfer Optimization module, which is used to construct agent objective functions embedded with physical conservation laws based on the governing equations in high-order tensor form; Specifically, after completing the aforementioned high-order tensor control equation construction and dynamic dimensionality reduction, the system further incorporates a physical constraint proxy modeling and migration optimization module to achieve efficient search and transferable optimization within the control parameter space. This module is structurally consistent with the tensorization of the control equations. Its core purpose is to rapidly evaluate and iteratively optimize key control parameters by constructing proxy objective functions that satisfy physical constraints, without directly relying on solving the complete high-dimensional control equations.

[0043] Traditional optimization methods typically solve high-dimensional control problems directly through iterative solutions of the original governing equations. While this approach offers strong physical consistency, it can be prone to computational convergence difficulties and unstable parameter searches when coupling is strong and the objective function is large-dimensional. This is particularly true in multi-objective control tasks. Therefore, this module, based on tensor structures, employs a weak form physical residual representation, supplemented by a Lagrangian constraint mechanism, enabling surrogate models to maintain physical consistency while also possessing sufficient structural flexibility and computational efficiency.

[0044] In this embodiment, the physical constraint agent modeling and migration optimization module takes the unified tensor control expression structure as input and first constructs a set of basic function sets , which is used to characterize the objective function response in the control parameter space. represents the control parameter vector, Indicates the As an option, the basis function set can be constructed based on Chebyshev basis, radial basis function, B-spline function, etc., and the specific form is not limited.

[0045] Specifically, the basis function training process satisfies the following weak form physical conservation constraints: ; in: Indicates the control area; represents the control operator constructed based on the partial derivative operator in the dimensionality-reduced tensor control equation; represents the time derivative of the basis function; Indicates the set weak solution tolerance constant, which is generally set in within the range.

[0046] In one possible implementation, in order to ensure that the objective function has differentiable continuity in the global spatial range, the basis function set also introduces adjacent time step coupling terms during training to satisfy the space-time synergy condition.

[0047] In the stage of constructing the agent objective function, the system performs a weighted combination of multiple basis functions to obtain the objective function form: ; in: represents the agent objective function; For the The coefficients of the basis functions; is the constrained Lagrange multiplier; represents the physical residual term constructed based on the tensor structure governing equations; Indicates the basis functions.

[0048] As an option, the residual term The following expressions can be used: ; in: 、 、 are the terms of the tensor control equation after dimensionality reduction; Represents the control variable tensor after dimensionality reduction; Indicates the Partial derivatives in spatial dimensions; Indicates time.

[0049] In some embodiments, to achieve rapid adaptation of the model across tasks and scales, the module can use a limited sample set to transfer and fine-tune the proxy objective function. Specifically, this can be done by minimizing the squared residual between the proxy function prediction and the actual numerical solution: ; in: Indicates the Sample control parameters; represents the reference value obtained by directly solving the original tensor governing equation under this parameter; Indicates the total number of samples.

[0050] Furthermore, the surrogate model is established by constructing a surrogate objective function that embeds physical conservation laws. This surrogate model receives control parameters as input and can quickly output system performance indicators. The output is the value of the surrogate objective function. Because physical constraints are incorporated into the model during training and construction, its prediction results are not only fast but also avoid absurd solutions that violate basic physical laws, ensuring the physical authenticity and reliability of the optimization results. Within the surrogate model structure, the system supports organizing the basis function set into a tensor form to be compatible with the aforementioned control structure, forming the following composite structure: ; in: Represents the fourth-order basis function weight tensor; is the result of tensor basis function combination; Indicates the control variables; is the tensor index.

[0051] The objective function output by this module serves as the input for the multi-objective optimization phase. Its residual structure is highly coupled to the implicitly coupled solution, ensuring physical consistency and structural stability throughout the optimization process. In some scenarios, this module also supports explicitly embedding surrogate functions into the constrained optimization process, allowing for the construction of hybrid nonlinear optimization systems.

[0052] Asynchronous time stepping and multi-scale coordination module, which is used to asynchronously advance the flow and heat transfer fields using different time steps based on the phase interface curvature tensor, and to implicitly solve the governing equations after dimensionality reduction using the Jacobian matrix in the form of a tensor product; Specifically, after completing the aforementioned tensor control equation construction, dynamic rank reduction, and physical constraint proxy model construction, the present invention systematically constructs an asynchronous time stepping and multiscale coordination module to further address the differences in the time distribution of response scales between different physical fields. This module, based on the phase interface structure tensor and low-rank tensor control expression as the core reference, mainly implements asynchronous propulsion strategies for different physical fields such as flow fields and heat transfer fields, and ensures the implicit strong coupling solution capability under asynchronous step conditions.

[0053] In general, the control variables in multiphase flow systems (such as velocity fields, temperature fields, and phase fields) exhibit significant differences in spatial scales and temporal evolution rates. Using a unified time stepping approach often results in decreased numerical efficiency and even coupling instability. To address this issue, this paper proposes an asynchronous step-size control strategy driven by the interface curvature tensor. Combining this with the aforementioned tensor structure coupling, this paper constructs a tensor increment solution method that adapts to each step size.

[0054] In this embodiment, the asynchronous time stepping and multi-scale coordination module first receives the curvature tensor provided by the tensor modeling module. , and the time step adjustment range of different physical fields is determined according to its norm. Specifically, the flow field time step Determined based on traditional CFL conditions: ; in: is the CFL number; represents the grid space step; Indicates the The velocity component in the direction.

[0055] As an option, the heat transfer field time step In this paper, a scaling strategy driven by the curvature tensor norm is adopted: ; in: is the curvature reference value, which is generally between; represents the Frobenius norm of the curvature tensor; To avoid small constants with zero denominators, we often take .

[0056] Specifically, as the severity of the interface change increases (i.e. increases), the heat transfer time step will be reduced accordingly to meet the stability requirements brought about by the enhanced conduction-convection coupling in the local area.

[0057] In one possible implementation, the module stores the state variables at different time step stages in a multi-level cache structure based on the above-mentioned unequal-step advancement strategy, and couples and solves all physical variable increments within each master time step using the following tensor joint structure: ; ; ; in: Indicates the update amount of each control variable; is the time derivative tensor of the tensor control equation after dimension reduction; denote the residual tensors of the momentum and energy equations respectively; is the phase field advancement step, which is the same as the flow field step or a multiple thereof; is the phase field diffusion coefficient; is the chemical potential, and its expression is derived from the free energy function.

[0058] As an option, the present invention adopts an embedded preconditioned conjugate gradient method (PCG) to solve the above tensor increment update process, so as to avoid the numerical tension generated during the asynchronous advancement process from destroying the overall strong coupling.

[0059] To further enhance timescale adaptability, some implementations allow for local timestep control for subgrids within different regions. This strategy dynamically constructs a subdomain advancement schedule by combining information such as the local curvature tensor, velocity modulus, and temperature gradient, significantly improving computational resource allocation efficiency without compromising global accuracy.

[0060] It should be noted that this module is deeply integrated with the Jacobian matrix in the form of the aforementioned tensor product, ensuring that the matrix-tensor joint solution interface under the corresponding rank structure can be implemented in each advancement.

[0061] The multi-objective optimization and decision mapping module is used to perform multi-objective optimization based on the results of the proxy objective function and the implicit strong coupling solution, and map the optimization results back to the original control parameter space.

[0062] Specifically, after constructing the aforementioned proxy objective function and solving it with asynchronous time marching, the system of the present invention ultimately coordinates the solution of different control objectives through a multi-objective optimization and decision mapping module. The resulting control parameters are then mapped back to the original physical space, enabling multi-dimensional feedback regulation of the system's controllability variables. This module is structurally coupled to the physical constraint proxy model and establishes a parameter mapping channel with the tensor dimensionality reduction model and implicit solver to achieve closed-loop control and optimization feedback.

[0063] In general, the simulation and control of multiphase coupled systems often require simultaneous consideration of multiple performance objectives, such as heat exchange efficiency, shear stability, and phase interface uniformity. These objectives may conflict with each other, and there is no single perfect solution that achieves optimality across all objectives. Instead, a set of non-inferior solutions, consisting of numerous optimal trade-offs, is required. No single solution in the set can improve the performance of a single objective without sacrificing the performance of at least one other objective. The specific set of input control parameters for each non-inferior solution in the set is called the non-inferior control parameter set. Specifically, a non-inferior solution is the optimal output of the system in the performance objective space, while the non-inferior control parameter set is the input combination that leads to these optimal outputs in the control parameter space. Traditional single-objective optimization strategies struggle to effectively address such multi-objective control requirements and are not directly scalable to high-dimensional tensor control structures. Therefore, this module employs a multi-objective optimization algorithm combined with surrogate function outputs to construct a Pareto frontier control solution. A structural mapping operator is then used to project the optimization results back to the original control parameter space.

[0064] In this embodiment, the multi-objective optimization and decision mapping module first receives the objective function output form from the physical constraint agent modeling and migration optimization module: ; in: Indicates the A proxy objective function; represents the control parameter vector; represents the proxy basis function; is the function coefficient under the corresponding target; is the constrained Lagrange multiplier under this objective; is the corresponding residual term.

[0065] In one possible implementation, this module defines multiple objective functions jointly as the following vector objective function system: subject to ; in: represents the total number of objective functions; For the The maximum residual tolerance allowed for a target; No. The physical residual term corresponding to the objective function.

[0066] As an alternative, the multi-objective optimization algorithm uses an evolutionary multi-objective strategy based on Pareto frontier search to construct a non-inferior solution set , where each element The following conditions must be met: ; in: There is no candidate solution ; is the decision variable vector (current solution, candidate solution); For the An objective function.

[0067] Specifically, in each optimization iteration, the system generates a new set of candidate solutions on the agent model through genetic crossover, mutation and selection operations, and updates the non-inferior solution frontier with a multi-objective ranking strategy (such as NSGA-II, MOEA / D). The non-inferior solution frontier corresponds to the preliminary non-inferior solution control parameter set.

[0068] In order to realize the back projection of the optimization results to the tensor control system, this module defines the following inverse mapping function: ; in: The spatial control coefficient vector of the agent obtained for optimization; represents the operator that maps from the surrogate basis function combination space back to the original control variable space; The original control variable vector is the actual physical parameter to be solved; the mapping relationship has established functional correspondence during the modeling process and has reversibility or numerical inversion characteristics.

[0069] In some embodiments, to improve mapping accuracy, the system of the present invention further introduces a constraint verification step after the non-inferior solution projection, and performs the following physical consistency evaluation on the mapping results: , and ; in: The final calibration tolerance set for each objective function; is the interface curvature tensor under the mapped control parameters; is the global curvature stability threshold.

[0070] As an implementation strategy, this module also supports organizing the non-inferior solution set structure through tensor encoding in actual deployment, so that it can be directly used for the next round of simulation initialization, forming a data-driven closed-loop structure.

[0071] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A multiphase flow control and heat transfer simulation system, characterized in that: include: A multi-physics tensor modeling module is used to reconstruct the control equations in a unified high-order tensor form based on the preset scalar or vector form of the control equations describing multiphase flow, heat transfer and phase field, and to extract the phase interface curvature tensor from the phase field control equations in the high-order tensor form; a dynamic tensor dimensionality reduction and implicit coupling solution module, configured to receive the control equations in the form of high-order tensors and the phase interface curvature tensor, perform dynamic rank dimensionality reduction on the control equations in the form of high-order tensors, and construct a Jacobian matrix in the form of a tensor product that matches the rank of the dimensionality reduction; A physical constraint agent modeling and migration optimization module for constructing an agent objective function embedded with physical conservation laws based on the control equations in the form of high-order tensors; an asynchronous time stepping and multi-scale coordination module for asynchronously advancing the flow field and the heat transfer field using different time steps based on the phase interface curvature tensor, and performing an implicit strong-coupling solution to the dimensionality-reduced governing equations using the Jacobian matrix in the form of the tensor product; The multi-objective optimization and decision mapping module is used to perform multi-objective optimization based on the results of the proxy objective function and the implicit strong coupling solution, and map the optimization results back to the original control parameter space.

2. A multiphase flow control and heat transfer simulation system according to claim 1, characterized in that: The multi-physics tensor modeling module includes: Obtaining a plurality of control equations for describing the evolution of the velocity field, the temperature field, and the phase field, and extracting control variables from the control equations; According to the spatiotemporal distribution dimensions of the control variables, a unified high-order tensor expression is constructed so that the control variables can be stored in a fourth-order tensor structure. The phase interface normal vector is calculated from the phase field tensor, and then the phase interface curvature tensor is calculated based on the vector, and the tensor is used as an indicator input for subsequent rank reduction and time step control.

3. A multiphase flow control and heat transfer simulation system according to claim 2, characterized in that: The phase interface curvature tensor calculation process includes: The interface normal distribution is calculated by combining the gradient and the normalized direction vector; The interface curvature tensor is obtained by calculating the second-order derivative of the normal vector tensor field; The curvature tensor is normed and time-domain smoothed for dynamic time step adjustment.

4. The multiphase flow control and heat transfer simulation system according to claim 1, characterized in that: The dynamic tensor dimensionality reduction and implicit coupling solution module includes: Determining the optimal decomposition rank of the high-order tensor expression based on the norm of the phase interface curvature tensor and the condition number of the current Jacobian matrix; Performing low-rank reconstruction on the high-order tensor expression using a tensor decomposition algorithm and generating a dimensionality-reduced tensor model; A Jacobian matrix in tensor product form matching the decomposition rank is constructed, and the Jacobian matrix is used in a subsequent iterative structure solving process.

5. A multiphase flow control and heat transfer simulation system according to claim 4, characterized in that: The tensor decomposition algorithm is a Tucker decomposition algorithm with rank adaptive adjustment, which includes: Initialize multiple tensor kernels and factor matrices, and set rank upper bounds and error thresholds; Dynamically adjust the decomposition rank according to the control tensor residual during each dimensionality reduction process; The iteration termination condition is determined based on the reconstruction error between the decomposed tensor and the original tensor.

6. The multiphase flow control and heat transfer simulation system according to claim 1, characterized in that: The physical constraint agent modeling and migration optimization module includes: Construct a set of basis functions for expressing tensor control relationships and perform physical consistency training on the basis function set to ensure that the basis function set satisfies the preset conservation law conditions; A surrogate objective function is constructed based on a linear combination of multiple basis functions, and this surrogate objective function is embedded into the tensor control framework as a surrogate model that can quickly predict system performance. A conservation error term is set and a Lagrange multiplier is introduced, and the residual is embedded into the objective function as an additional constraint for subsequent optimization solution.

7. A multiphase flow control and heat transfer simulation system according to claim 6, characterized in that: The construction process of the proxy objective function includes: The surrogate function is trained with weak form integral residuals in multiple known sample scenarios; The time derivative of the field variable is introduced to construct the deviation term with the physical operator term in the tensor control equation; Control the residuals on all basis functions to not exceed a preset physical tolerance threshold.

8. The multiphase flow control and heat transfer simulation system according to claim 1, characterized in that: The asynchronous time stepping and multi-scale coordination module includes: Determine the local time step of the flow field based on the current flow field velocity distribution and the computational domain spatial step; Calculate the norm of the interface curvature tensor and adjust the time step of the heat transfer field based on this value to achieve dynamic matching of time scales between different physical fields; Independent time steps are used for the control equations corresponding to different control variables, and tensor increments are solved simultaneously in each step.

9. The multiphase flow control and heat transfer simulation system according to claim 6, characterized in that: The multi-objective optimization and decision mapping module includes: Setting a plurality of performance objective functions for measuring simulation results, and uniformly embedding the objective functions into the agent model; Under the condition of maintaining physical conservation constraints, a multi-objective optimization algorithm is used to search for a non-inferior solution set in the control parameter space. The non-inferior solution set consists of a set of optimal solutions that cannot be replaced by each other, and each optimal solution corresponds to a set of input control parameters, forming a non-inferior solution control parameter group; The non-inferior solution control parameter group is mapped to the original control parameter space in the space of the proxy model, and a constraint consistency check is performed.

10. The multiphase flow control and heat transfer simulation system according to claim 9, characterized in that: The multi-objective optimization algorithm adopts an evolutionary multi-objective optimization method based on Pareto frontier search, including: Construct a joint evaluation index of the objective function value and the residual constraint term based on the output results of the surrogate model; Perform Pareto sorting on the search results and screen the frontier of non-inferior solutions; The non-inferior solution control parameter group is input into the simulation system for re-calibration to determine the optimal mapping result.

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