A computational fluid dynamics error propagation prediction and control method and apparatus

Abstract

This invention discloses a method and apparatus for predicting and controlling error propagation in computational fluid dynamics (CFD), belonging to the field of CFD numerical simulation technology. Addressing the problems of existing technologies' difficulty in identifying error propagation paths in advance and the lack of proactive control measures, this invention constructs an error propagation state characterization model, representing the propagation behavior of numerical errors under physical mechanisms such as convection, diffusion, and reaction as a combination of multiple error propagation modes; it predicts the error propagation velocity, direction, and propagation length by combining local flow field physical parameters; it constructs an error propagation risk criterion to identify potential error growth regions; and it implements adaptive strategies such as local time step adjustment, adaptive mesh refinement, enhanced numerical scheme stability, and rigid control of the reaction zone. This invention can identify and proactively control unstable regions before significant error amplification, significantly improving the stability and reliability of numerical simulations of complex flows and combustion.

Description

Technical Field

[0001] This invention belongs to the field of computational fluid dynamics numerical simulation and scientific computing technology, specifically relating to a method and apparatus for predicting and controlling error propagation in computational fluid dynamics. Background Technology

[0002] Computational fluid dynamics (CFD) is an important numerical tool for studying complex flow and heat and mass transfer processes. It has been widely used in aerodynamic design of aero-engines, combustion process simulation, high-temperature reactive flow analysis, and the study of multi-physics coupled flow problems. In engineering problems such as aero-engine combustion simulation, CFD needs to solve the multi-physics coupled control equations of convection, diffusion, and chemical reaction simultaneously. The calculation process is highly nonlinear and multi-scale.

[0003] Numerical calculations inevitably introduce discretization truncation errors, time integration errors, grid resolution errors, and physical model approximation errors. These errors propagate, superimpose, and even amplify within the flow field through mechanisms such as convection, diffusion, and chemical reactions, significantly impacting the stability and reliability of the numerical results. Particularly in problems involving high-temperature reactive flows or turbulent combustion simulations, the strongly nonlinear reaction processes and multi-scale structures within the flow field further complicate error propagation. Rapid growth of local errors can easily lead to computational instability or even numerical divergence.

[0004] Current CFD numerical simulations primarily assess and control numerical errors through methods such as residual monitoring, mesh convergence analysis, adaptive mesh refinement, and time step control. For example, monitoring changes in the residuals of conservation equations is used to determine computational convergence; mesh refinement or adaptive meshing methods are used to improve local resolution; or the time step is reduced to enhance numerical stability. However, these methods are mostly post-evaluation or passive adjustment mechanisms, meaning that judgment and adjustments are typically made only after errors have occurred and begun to affect the computation, using residual changes or convergence indices. For complex multiphysics coupled flows, numerical errors often propagate along characteristic flow field structures, such as downstream transport via convection, diffusion along gradient directions, or rapid amplification in the reaction region. Existing methods typically struggle to identify the propagation path and growth trend of errors in advance and lack the ability to predict error propagation behavior. Therefore, in complex flow and combustion numerical simulations, an effective method remains lacking that can uniformly characterize numerical error propagation behavior and achieve early prediction and proactive control.

[0005] Therefore, how to effectively describe the propagation characteristics of numerical errors during CFD calculations and predict and control the error growth trend during the calculation process, thereby improving the stability and reliability of numerical simulations of complex flows, has become an important technical problem that urgently needs to be solved in the field of computational fluid dynamics. Summary of the Invention

[0006] The purpose of this invention is to address the problems in existing computational fluid dynamics numerical simulations, such as the difficulty in identifying numerical error propagation behavior in advance, the difficulty in effectively characterizing error growth mechanisms, and the lack of active control methods. This invention provides a method and apparatus for predicting and controlling error propagation in computational fluid dynamics. By constructing an error propagation state characterization model, the propagation characteristics of errors under physical mechanisms such as convection, diffusion, and chemical reactions are uniformly described. The method predicts error propagation trends, establishes risk criteria, and implements adaptive control to improve the stability and reliability of numerical simulations of complex flows and combustion.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a method for predicting and controlling error propagation in computational fluid dynamics, comprising the following steps: Step 1: Establish a CFD numerical calculation model and obtain flow field state information, which includes conserved variables, local flow field gradient, characteristic velocity, and reaction rate; Step 2: Extract numerical error characterization quantities and local flow field physical characteristics during the CFD solution process. The numerical error characterization quantities include discrete residuals and local numerical fluctuation characteristics. The local numerical fluctuation characteristics include the changes in conserved variables between adjacent grid cells or adjacent time steps. The local flow field physical characteristics include one or more of the following: local flow field gradient, local characteristic velocity, local diffusion coefficient, local reaction intensity, and local time scale. Step 3: Construct an error propagation state representation model to represent the evolution of numerical errors under different propagation mechanisms as a combination of multiple error propagation modes; Step 4: Based on the error propagation state characterization model and combined with local flow field physical parameters, predict the propagation trend of the error in space and time, including the error propagation speed, propagation direction and propagation length; Step 5: Construct error propagation risk criteria based on error propagation prediction results and identify potential error growth areas; Step Six: Implement adaptive control strategies for the identified potential error growth regions. The adaptive control strategies include one or more of the following: local time step adjustment, adaptive mesh refinement, numerical format stability enhancement, and rigid control of the reaction zone.

[0009] Furthermore, in step three, the error propagation state characterization model is realized by constructing an error propagation state vector, which represents a weighted combination of multiple error propagation modes, including at least convection propagation mode, diffusion propagation mode, and reaction amplification mode.

[0010] Furthermore, the intensity of the convection propagation mode is characterized as follows:

[0011] The intensity of the diffusion propagation mode is characterized as follows:

[0012] The intensity of the reaction amplification mode is characterized as follows:

[0013] in, For local characteristic velocities, For local gradient intensity, The local diffusion coefficient is... For local grid size, The intensity of the local reaction. The preset small quantity is greater than zero; the intensity of each mode is normalized using the following formula to obtain the state coefficients:

[0014] in, These are the normalized modal coefficients. This represents the total number of error propagation modes.

[0015] Furthermore, in step four, the formula for calculating the error propagation speed is:

[0016] in, For the local equivalent error propagation speed, , , These are the state coefficients for convection, diffusion, and reaction modes, respectively. For local reaction timescales, For a preset small quantity greater than zero, For local characteristic velocities, The local diffusion coefficient is... This refers to the local mesh size; The direction of propagation is represented by the following unit vector:

[0017] in, Let the local error propagation direction be the unit vector. For the direction of flow transport, For local error intensity, This represents the direction of the error propagation trend from the high-value region to the neighboring region. The effect of changes in reaction intensity on the direction of error growth; The formula for calculating the propagation length is:

[0018] in, For local propagation length, For time step.

[0019] Furthermore, in step five, the calculation formula for the error propagation risk criterion is as follows:

[0020] in, For the first Error propagation risk index for each grid cell For local error intensity, For local gradient intensity, For local propagation length, , , , These are non-negative weighting coefficients. For reference error strength, For reference gradient strength, For the local minimum physical time scale, For local grid size, For a preset small quantity greater than zero, For time step; when When the risk threshold is exceeded, the corresponding grid cell will be identified as a high-risk error propagation area.

[0021] Furthermore, in step six, the local time step adjustment is adaptively reduced according to the risk intensity; the higher the risk, the smaller the time step. The adaptive mesh refinement is performed when the risk exceeds the mesh refinement threshold. The numerical format stability enhancement is achieved by increasing the local numerical dissipation coefficient or the limiter strength. The reaction zone rigid control uses implicit integration or substep integration for regions where the state coefficient of the reaction amplification mode exceeds the preset mode threshold and the risk index exceeds the preset risk threshold.

[0022] Furthermore, the method repeats steps one through six at each time step or every few time steps to form a closed-loop mechanism for error propagation prediction, judgment, and control.

[0023] Furthermore, the method is applicable to CFD numerical solutions for compressible reactive flows, incompressible flows, turbulent combustion simulations, and multi-physics coupled flows.

[0024] In a second aspect, the present invention provides a computational fluid dynamics error propagation prediction and control device, comprising: The flow field information acquisition module is used to establish a CFD numerical calculation model and acquire flow field state information; The error characterization extraction module is used to extract numerical error characterization quantities during the CFD solution process; The error propagation state modeling module is used to construct an error propagation state representation model; The error propagation trend prediction module is used to predict the speed, direction, and length of error propagation. The risk criterion construction module is used to construct error propagation risk criteria based on prediction results and identify high-risk areas. The adaptive control module is used to implement adaptive control strategies in high-risk areas.

[0025] Furthermore, the adaptive control module includes a local time step adjustment unit, a mesh adaptive refinement unit, a numerical format stability enhancement unit, and a reaction zone rigid control unit. Each unit is selectively activated or activated in combination based on the risk criterion results.

[0026] Compared with the prior art, the present invention has the following beneficial effects: 1. By constructing an error propagation state characterization model, this invention can uniformly characterize the propagation behavior of numerical errors in different physical mechanisms such as convection, diffusion, and reaction, overcoming the shortcomings of traditional methods in uniformly describing the propagation behavior of errors in different physical mechanisms; 2. This invention predicts the propagation trend of error in space and time by combining information such as flow field gradient, characteristic velocity and local time scale. It can predict the error propagation trend in advance, identify potential unstable areas before the error is significantly amplified, and achieve forward control. 3. By establishing an error propagation risk criterion and implementing an adaptive control strategy for potentially unstable regions, this invention helps to suppress the rapid spread and amplification of errors during the calculation process, and significantly improves the stability of numerical simulations of complex flows (especially combustion and multi-physics coupling problems). 4. By predicting and controlling the error propagation behavior during the numerical calculation process, this invention can reduce the impact of error propagation on the calculation results, making the CFD simulation results more stable and reliable. It is particularly suitable for high-precision numerical simulation of multi-scale, multi-physics coupled problems such as aero-engine combustion. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1This is a flowchart illustrating a computational fluid dynamics error propagation prediction and control method according to an embodiment of the present invention. Detailed Implementation

[0029] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0030] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0031] This invention provides a computational fluid dynamics error propagation prediction and control method, which is applicable to CFD numerical solutions for compressible reactive flows, incompressible flows, turbulent combustion simulations, and multi-physics coupled flows.

[0032] This invention uses the compressible reactive flow within an aero-engine combustion chamber as an example to illustrate the solution of this invention in detail. For example... Figure 1 As shown, the method described in this embodiment of the invention includes the following steps: Step 1: Establish a CFD numerical calculation model and obtain flow field state information This step establishes and numerically discretizes the corresponding CFD governing equations for the target flow problem to obtain flow field state information. This information includes conserved variables, local flow field gradients, characteristic velocities, and reaction rates, providing fundamental data for error propagation analysis. The conserved variables include physical variables such as velocity, pressure, temperature, and component concentration.

[0033] Specifically, for general compressible reactive flow, its governing equations can be written in a conservation form:

[0034] In formula (1), The vector of conserved variables may include density, momentum, total energy, and the mass fraction of each component, etc. For time; For the quantity of goods and services; For diffusion flux; This is the source term vector, which in combustion problems can include chemical reaction source terms, volume force source terms, etc. This represents the divergence operator.

[0035] For the i-th control volume on the discrete mesh, spatial discretization is performed using finite volume, finite difference, or finite element methods, and the discrete update relation is obtained by solving it using explicit or implicit time-progression methods:

[0036] In formula (2), Indicates the first The time step Conserved variables on each grid cell; This represents the conserved variable after the next time step update; For time step; , , They represent the first time. The time step, the first Discretization results of convection, diffusion, and source terms on each grid cell.

[0037] The above formulas (1) and (2) form the computational basis for error identification and propagation analysis.

[0038] Step 2: Extracting local error characterization quantities and flow field physical characteristic quantities This step extracts numerical error characteristics during the CFD solution process. These numerical error characteristics include discrete residuals and local numerical fluctuation features. The local numerical fluctuation features include the changes in conserved variables between adjacent grid cells or adjacent time steps.

[0039] Specifically, during each time step, local discrete residuals are calculated for each grid cell to characterize the instantaneous level of numerical error. The residual of a grid cell can be defined as:

[0040] In formula (3), For the first The grid cell in the first... The discrete residual vector at each time step, when the discrete solution completely satisfies the discrete conservation equation. Ideally, it should be close to zero; The larger the magnitude, the greater the degree of local discrete error or numerical imbalance.

[0041] To form a scalarized representation of local error, we can define:

[0042] In formula (4), For the first The grid cell in the first... The intensity of local error at each time step; This represents the L2 norm.

[0043] Local numerical fluctuation characteristics include changes in conserved variables between adjacent grid cells, such as computational cells. and neighboring units Between and the change in the same unit between adjacent time steps. These fluctuation characteristics are used to help determine the local non-uniformity of the error.

[0044] In addition to the aforementioned local residuals, this embodiment of the invention also extracts local flow field physical characteristics related to error propagation, including local flow field gradient, local characteristic velocity, local diffusion coefficient, local reaction intensity, and local time scale. Specifically: 1) Local flow field gradient index For the first For each grid cell, the gradient intensity of the conserved variable or the primary physical variable can be defined as follows:

[0045] In formula (5), For local gradient intensity; For the first The gradient vector or gradient tensor of the variables on each grid cell; the larger the gradient, the more drastic the change in the local flow field, and the easier it is for errors to accumulate and propagate in that region.

[0046] 2) Local characteristic velocity Definition of the first The local characteristic velocity of each grid cell is:

[0047] In formula (6), Local characteristic velocity; This is the local fluid velocity vector; The magnitude of the flow velocity; The local sound velocity is used because, in compressible flow, error propagation is usually related to both the flow velocity and the propagation speed of pressure disturbances. Therefore, a combination of flow velocity and sound velocity is used to characterize the local characteristic velocity.

[0048] 3) Characteristic quantity of local diffusion coefficient For problems with significant diffusion effects, the local diffusion coefficient can be defined as follows: In multi-component or thermal diffusion problems, It can represent the equivalent mass diffusion coefficient, thermal diffusion coefficient, or viscous diffusion scale.

[0049] 4) Local reaction intensity index For the reactive flow problem, the local reaction intensity is defined as:

[0050] In formula (7), Local reaction intensity; For the first Component generation rate vector or source term vector on each grid cell; The larger the value, the more intense the local chemical reaction, and the more likely the error will be amplified rapidly in that region.

[0051] 5) Local time scale The timescale of local physical processes can be estimated separately according to different mechanisms. For example: Convection timescale:

[0052] Diffusion timescale:

[0053] Reaction timescale:

[0054] In formulas (8), (9), and (10), , , These represent the local convection timescale, the local diffusion timescale, and the local reaction timescale, respectively. For the first The characteristic grid size (i.e., local grid size) of each grid cell; The preset small quantity is greater than zero, specifically to prevent small positive numbers with a denominator of zero; the smaller a certain time scale, the stronger the control of the corresponding physical mechanism over the local evolution.

[0055] The above local error intensity Local gradient intensity Local diffusion coefficient Local reaction intensity Local convection timescale Local diffusion timescale and local reaction time scale Together, they constitute the input information for subsequent error propagation state modeling.

[0056] It should be noted that in the embodiments of this invention, "local" refers to a physical quantity or computational quantity defined for a single grid cell (control volume). CFD numerical calculation discretizes the computational domain into multiple grid cells, each with independent coordinates, dimensions, and physical variables. Terms prefixed with "local," such as "local flow field gradient," "local characteristic velocity," "local error intensity," "local diffusion coefficient," "local grid size," "local response intensity," and "local time step," indicate that the quantity is calculated or defined on a single grid cell, rather than as a global average or a global quantity. For example, the local flow field gradient refers to the... The spatial rate of change of conserved variables (such as velocity and pressure) within a grid cell; local characteristic velocity refers to the sum of the fluid velocity and the speed of sound within that cell (for compressible flow) or the flow velocity (for incompressible flow). This cell-by-cell definition method enables the present invention to achieve spatially differentiated error propagation analysis and control.

[0057] Step 3: Construct an error propagation state representation model This step constructs an error propagation state vector to represent the evolution of numerical errors under different propagation mechanisms as a combination of multiple error propagation modes. By constructing the error propagation state vector, the propagation characteristics of errors in physical mechanisms such as convection transport, diffusion processes, and chemical reactions are uniformly described.

[0058] In one embodiment, drawing on the concept of quantum superposition, the error propagation state is represented as a multimodal combination form, without relying on real quantum computing hardware.

[0059] Specifically, the definition of the first The grid cell in the first... The error propagation state at each time step is as follows:

[0060] In formula (11), Indicates the first Error propagation state of each grid cell; This is a symbol for a state vector, used to represent an abstract modal state, which does not represent a real quantum mechanical particle state; This represents the total number of error propagation modes. For the first Error propagation modes; For the first The state coefficients corresponding to a mode are used to characterize the importance of that mode in the propagation of local errors.

[0061] In a typical embodiment, take This corresponds to the following three basic modes: : Convection propagation mode; : Diffusion propagation mode; : Response amplification modes. Then calculate the original intensity of each mode: Original intensity of convection propagation mode:

[0062] In formula (12), The intensity of the convection propagation mode, For local characteristic velocities, The local gradient strength is the greatest local characteristic velocity and the stronger the gradient, the more pronounced the tendency for the error to be transported and spread along the flow direction.

[0063] Original strength of the diffusion propagation mode:

[0064] In formula (13), For the intensity of the diffusion propagation mode, For local gradient intensity, The local diffusion coefficient is... For local grid size, The preset value is a small amount greater than zero; the larger the diffusion coefficient, the larger the gradient, and the coarser the mesh, the more obvious the impact of error diffusion and propagation in the neighboring region.

[0065] Original strength of the reaction amplification mode:

[0066] In formula (14), To reflect the intensity of the amplified mode, The intensity of the local reaction. The local gradient strength is denoted as ; in regions where strong reactions and strong gradients coexist, local errors are easily amplified rapidly by the effect of rigid source terms.

[0067] Based on this, the original intensity of each mode is normalized to obtain the state coefficients:

[0068] In formula (15), This represents the total number of error propagation modes. A preset small quantity that is greater than zero; The normalized modal coefficients satisfy... And there are

[0069] Formulas (15) and (16) enable the error propagation effects under different physical mechanisms to be compared and characterized within a unified framework.

[0070] Step 4: Predict the propagation trend of error This step, based on the error propagation state characterization model and combined with local flow field physical parameters (such as gradient information, flow characteristic velocity, and reaction time scale), predicts the propagation trend of error in space and time. The propagation trend includes error propagation speed, propagation direction, and propagation length, thereby identifying regions where errors may rapidly spread or amplify.

[0071] Specifically, after obtaining the local error propagation state, the propagation direction, propagation speed, and propagation scale of the error can be further estimated.

[0072] 1) Local error propagation speed Definition of the first The equivalent error propagation speed of each grid cell is:

[0073] In formula (17), Local equivalent error propagation speed , , These are the state coefficients for convection, diffusion, and reaction modes, respectively. For local reaction timescales, For a preset small quantity greater than zero, For local characteristic velocities, The local diffusion coefficient is... This refers to the local mesh size; This indicates the error transport velocity dominated by convection; This indicates the rate of error propagation dominated by diffusion. This represents the equivalent contribution of error growth to local propagation under reaction-dominated conditions; this equivalent velocity is not the actual fluid velocity, but rather an equivalent index used to characterize the ability of error to spread in a local region.

[0074] 2) Local propagation direction The direction of error propagation is usually related to the gradient direction of the local solution and the flow direction. The propagation direction vector is defined as:

[0075] In formula (18), Let the local error propagation direction be the unit vector. For the direction of flow transport, For local error intensity, This represents the direction of the error propagation trend from the high-value region to the neighboring region. This represents the effect of changes in reaction intensity on the direction of error growth.

[0076] 3) Local propagation length Within one time step, the equivalent propagation length of the error in the local region can be defined as:

[0077] In formula (19), The local propagation length represents the local spatial scale that the error may affect within a time step. For time step. If the error is comparable to or significantly larger than the grid scale, it indicates a strong risk of local error propagation across cells.

[0078] Using the above formulas (17) to (19), the propagation trend of error in space and time can be quantitatively estimated, instead of being limited to the ex-post observation of traditional residuals.

[0079] Step 5: Constructing the error propagation risk criterion This step constructs an error propagation risk criterion based on the error propagation prediction results, identifies potential numerically unstable regions in the CFD calculation process, and identifies potential error growth regions, providing a basis for subsequent error control strategies.

[0080] Specifically, this risk criterion comprehensively considers local error intensity, gradient intensity, propagation velocity, and local physical rigidity. Therefore, the calculation formula for the error propagation risk criterion is:

[0081] In formula (20), For the first Error propagation risk indicators for each grid cell; Local error intensity; For local gradient intensity; This is the local propagation length; , , , These are non-negative weighting coefficients used to adjust the influence intensity of different factors; This serves as a reference error strength. For reference gradient strength; This refers to the local mesh size; A preset small quantity that is greater than zero; For time step; For a local minimum physical timescale, it can be defined as:

[0082] In this embodiment of the invention, the reference error intensity and reference gradient strength Reference values ​​used to make local error intensity and local gradient intensity dimensionless. The initial average error, the initial maximum error, or a threshold set by the user based on experience can be used. Similarly, the initial average gradient or characteristic gradient can be used. Introducing a reference value makes the various aspects of the risk criterion comparable.

[0083] In formula (20), the first term represents the current local error level; the second term represents the local flow field non-uniformity; the third term represents the influence intensity of error propagation on the neighboring grid; and the fourth term represents the degree of matching between the time step and the time scale of the local strongest control mechanism.

[0084] when Exceeding the preset risk threshold When this occurs, the grid cell can be identified as a high-risk error propagation region, i.e.: Then the corresponding number Each grid is a high-risk area. It can be set according to the type of calculation case, empirical parameters, or pre-calibrated results.

[0085] Step Six: Implement Error Propagation Control Strategies This step implements an adaptive control strategy for the identified potential error growth regions to suppress the rapid propagation and amplification of errors in the flow field. The adaptive control strategy includes one or more of the following: local time step adjustment, adaptive mesh refinement, numerical scheme stability enhancement, and rigid control of the reaction zone.

[0086] Specifically, once a high-risk error propagation region is identified, proactive controls are implemented in the corresponding region to reduce the risk of rapid error spread, amplification, or inducing numerical divergence. Control strategies may include one or more of the following.

[0087] 1) Local time step adjustment For high-risk areas, the time step is adaptively reduced according to the risk intensity, i.e., the local or global time step is reduced. The new time step can be defined as:

[0088] In formula (22), This is the adjusted local time step; This is the time step adjustment coefficient; when The larger the value, the smaller the new time step; that is, the higher the risk, the smaller the time step.

[0089] If a globally unified timeframe is used, adjustments can also be made based on the maximum risk value across the entire event:

[0090] In formula (23), This is the adjusted global time step. This is the global adjustment coefficient. .

[0091] 2) Adaptive Mesh Refinement Local mesh refinement is applied to high-risk areas to improve spatial resolution and reduce discretization and cross-cell propagation errors. The refined criteria can be written as: Then for the first Each grid undergoes grid refinement. The mesh refinement threshold is typically set to be greater than the preset risk threshold. The value of .

[0092] 3) Enhanced stability of numerical formats For high-risk areas, a more stable flux reconstruction scheme, limiter, or dissipation control parameter can be switched to. The numerical stability adjustment parameter is defined as follows: ,but

[0093] In formula (24), These are the adjusted numerical stability parameters; This represents the numerical dissipation coefficient, limiter strength parameter, or stability-related control parameter. This is the stability adjustment coefficient. Higher risks can be mitigated by increasing the local numerical dissipation coefficient or the limiter strength to enhance the stability of the numerical scheme, thereby increasing the local numerical stability control strength.

[0094] 4) Rigid control of the reaction zone For regions where the reaction amplification mode is dominant and the risk is high, i.e., for the state coefficients of the reaction amplification mode... Exceeding the preset modal threshold And risk indicators Exceeding the preset risk threshold In the region where the equation is in a certain range, further source term integration stabilization measures are adopted, such as local implicit integration, substep integration, or rigid correction strategies, to enhance the stability of the rigid equation. The criterion can be written as: and When this criterion is met, the more robust reaction integral method is preferentially applied to this region.

[0095] In this embodiment of the invention, steps one through six are repeated at each time step or several time steps (e.g., every five time steps). Specifically, the flow field is first updated to obtain the flow field state information for the current time step (step one); then, error characterization quantities are extracted (step two); an error state characterization model is constructed (step three); the propagation trend is predicted (step four); risk criteria are calculated (step five); and control strategies are executed (step six). This forms a continuous prediction-determination-control closed-loop mechanism until the calculation converges or a preset time is reached. This closed-loop mechanism of error propagation analysis and numerical control allows control actions to be triggered before the error significantly amplifies, thereby enhancing the numerical stability and computational reliability in complex flows, especially high-temperature reactive flows and aero-engine combustion simulations.

[0096] The method described in this invention can be integrated into existing CFD solvers, including but not limited to compressible flow solvers, reactive flow solvers, and turbulent combustion solvers based on the finite volume method, finite difference method, and finite element method. For different application scenarios, the number of error propagation modes, the composition of risk indicators, the threshold setting method, and the combination of control strategies can be adjusted according to actual needs. For example, in non-reactive flow problems, the reaction amplification mode can be omitted, retaining only the convection propagation mode and the diffusion propagation mode; in weakly compressible flow problems, local characteristic velocities can also be represented solely by the velocity modulus; in numerical simulation of aero-engine combustion, error propagation risk monitoring and control can be implemented by focusing on the high-temperature reaction zone, shear mixing layer, and strong gradient region. Therefore, the method described in this invention has good engineering applicability and scalability, and is suitable for various CFD numerical simulation scenarios such as complex flows, multi-physics coupled flows, and high-temperature reactive flows.

[0097] This invention also provides a computational fluid dynamics error propagation prediction and control device for implementing the above method, the device comprising: Flow field information acquisition module: used to execute step one, establish a CFD numerical calculation model and acquire flow field state information.

[0098] Error characterization extraction module: used to execute step two, extracting discrete residuals and local numerical fluctuation characteristics during the CFD solution process.

[0099] Error propagation state modeling module: used to execute step three, construct the error propagation state representation model, and calculate the state coefficients of each mode.

[0100] Error propagation trend prediction module: used to execute step four, predicting the error propagation speed, direction and propagation length.

[0101] Risk Criterion Construction Module: Used to execute step five, construct error propagation risk criteria (calculate risk indicators) based on the prediction results and identify high-risk areas.

[0102] Adaptive control module: Used to execute step six, implementing adaptive control strategies such as local time step adjustment, adaptive mesh refinement, numerical format stability enhancement, and rigid control of the reaction zone in high-risk areas.

[0103] The adaptive control module further includes a local time step adjustment unit, a mesh adaptive refinement unit, a numerical format stability enhancement unit, and a reaction zone rigid control unit. Each unit can be selectively activated or activated in combination based on the risk criterion results. For example, when the risk index exceeds a preset risk threshold but does not exceed a mesh refinement threshold, only the time step adjustment unit is activated; when the risk index exceeds both the mesh refinement threshold and the reaction mode coefficient exceeds a preset mode threshold, the local time step adjustment, mesh adaptive refinement, and reaction zone rigid control units can be activated in combination.

[0104] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, various modifications and variations can be made to the embodiments of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A computational fluid dynamics error propagation prediction and control method, characterized in that, Includes the following steps: Step 1: Establish a CFD numerical calculation model and obtain flow field state information, which includes conserved variables, local flow field gradient, characteristic velocity, and reaction rate; Step 2: Extract numerical error characterization quantities and local flow field physical characteristics during the CFD solution process. The numerical error characterization quantities include discrete residuals and local numerical fluctuation characteristics. The local numerical fluctuation characteristics include the changes in conserved variables between adjacent grid cells or adjacent time steps. The local flow field physical characteristics include one or more of the following: local flow field gradient, local characteristic velocity, local diffusion coefficient, local reaction intensity, and local time scale. Step 3: Construct an error propagation state representation model to represent the evolution of numerical errors under different propagation mechanisms as a combination of multiple error propagation modes; Step 4: Based on the error propagation state characterization model and combined with local flow field physical parameters, predict the propagation trend of the error in space and time, including the error propagation speed, propagation direction and propagation length; Step 5: Construct error propagation risk criteria based on error propagation prediction results and identify potential error growth areas; Step Six: Implement adaptive control strategies for the identified potential error growth regions. The adaptive control strategies include one or more of the following: local time step adjustment, adaptive mesh refinement, numerical format stability enhancement, and rigid control of the reaction zone.

2. The method according to claim 1, characterized in that, In step three, the error propagation state characterization model is realized by constructing an error propagation state vector, which represents a weighted combination of multiple error propagation modes, including at least convection propagation mode, diffusion propagation mode, and reaction amplification mode.

3. The method according to claim 2, characterized in that, The intensity of the convection propagation mode is characterized as follows: The intensity of the diffusion propagation mode is characterized as follows: The intensity of the reaction amplification mode is characterized as follows: in, For local characteristic velocities, For local gradient intensity, The local diffusion coefficient is... For local grid size, The intensity of the local reaction. The preset small quantity is greater than zero; the intensity of each mode is normalized using the following formula to obtain the state coefficients: in, These are the normalized modal coefficients. This represents the total number of error propagation modes.

4. The method according to claim 1, characterized in that, In step four, the formula for calculating the error propagation speed is: in, For the local equivalent error propagation speed, , , These are the state coefficients for convection, diffusion, and reaction modes, respectively. For local reaction timescales, For a preset small quantity greater than zero, For local characteristic velocities, The local diffusion coefficient is... This refers to the local mesh size; The direction of propagation is represented by the following unit vector: in, Let the local error propagation direction be the unit vector. For the direction of flow transport, For local error intensity, This represents the direction of the error propagation trend from the high-value region to the neighboring region. The effect of changes in reaction intensity on the direction of error growth; The formula for calculating the propagation length is: in, For local propagation length, For time step.

5. The method according to claim 1, characterized in that, In step five, the calculation formula for the error propagation risk criterion is as follows: in, For the first Error propagation risk index for each grid cell For local error intensity, For local gradient intensity, For local propagation length, , , , These are non-negative weighting coefficients. For reference error strength, For reference gradient strength, For the local minimum physical time scale, For local grid size, For a preset small quantity greater than zero, For time step; when When the risk threshold is exceeded, the corresponding grid cell will be identified as a high-risk error propagation area.

6. The method according to claim 1, characterized in that, In step six, the local time step adjustment is adaptively reduced according to the risk intensity; the higher the risk, the smaller the time step. The adaptive mesh refinement is performed when the risk exceeds the mesh refinement threshold. The numerical format stability enhancement is achieved by increasing the local numerical dissipation coefficient or the limiter strength. The reaction zone rigid control uses implicit integration or substep integration for regions where the state coefficient of the reaction amplification mode exceeds the preset mode threshold and the risk index exceeds the preset risk threshold.

7. The method according to claim 1, characterized in that, The method repeats steps one through six at each time step or every few time steps to form a closed-loop mechanism for error propagation prediction, judgment, and control.

8. The method according to claim 1, characterized in that, The method is applicable to CFD numerical solutions for compressible reactive flows, incompressible flows, turbulent combustion simulations, and multi-physics coupled flows.

9. A computational fluid dynamics error propagation prediction and control device, characterized in that, include: The flow field information acquisition module is used to establish a CFD numerical calculation model and acquire flow field state information; The error characterization extraction module is used to extract numerical error characterization quantities during the CFD solution process; The error propagation state modeling module is used to construct an error propagation state representation model; The error propagation trend prediction module is used to predict the speed, direction, and length of error propagation. The risk criterion construction module is used to construct error propagation risk criteria based on prediction results and identify high-risk areas. The adaptive control module is used to implement adaptive control strategies in high-risk areas.

10. The apparatus according to claim 9, characterized in that, The adaptive control module includes a local time step adjustment unit, a mesh adaptive refinement unit, a numerical format stability enhancement unit, and a reaction zone rigid control unit. Each unit is selectively or combined to start based on the risk criterion results.

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