Multi-medium fluid interaction state prediction system, method and equipment

Abstract

The invention relates to a multi-medium fluid interaction state prediction system, method and equipment, and aims to complete deep learning modeling under physical constraints by embedding a control equation and constraint conditions of multi-medium Riemannian solution into a loss function and a structure of a neural network, realize a PINNs-based multi-medium accurate Riemannian solver and realize multi-medium fluid interaction state prediction. A mapping relation between an input variable and an output variable is trained and learned through a physical information neural network, an output result strictly complies with physical constraints specified by the Riemannian problem, the spatial dimension of a solution is reduced, convergence is accelerated, finally, numerical simulation of multi-medium interaction of a complex engineering case is achieved under an Euler framework, and the method has the advantages of being high in practicability and easy to popularize. The multi-medium Riemannian problem can be stably and accurately solved, the state after multi-medium interaction is predicted, the prediction precision is higher, and the method is suitable for media with complex state equations.

Description

Technical Field

[0001] The present invention belongs to the technical field of fluid state prediction, and relates to a state prediction system, method and device for multi-media fluid interaction. Background Art

[0002] In the field of high-speed transient fluid dynamics, especially in complex non-equilibrium flows such as shock wave propagation and interface instability evolution under extreme loads, the study of multi-media coupling problems has important scientific value and engineering application significance. The core challenge lies in the high-precision description of the kinematic characteristics of the medium interface, which directly restricts the development of interface instability and the evolution of multiphase flow fields. Studies have shown that the multi-media Riemann solver constructed based on the hyperbolic conservation law system can effectively improve the numerical fidelity of the mass, momentum and energy transport process across the medium boundary by accurately characterizing the coupling mechanism at the interface.

[0003] Multi-medium Riemann solvers are often combined with numerical methods to construct interface models. They can be used to calculate the numerical flux of material interfaces and directly define the interface conditions in the ghost fluid method (GFM). GFM-based methods (such as the improved GFM (MGFM), the real GFM (RGFM), and the practical GFM (PGFM)) based on Riemann solutions are highly robust and suitable for challenging problem scenarios such as large contact discontinuities and strong pressure jumps at interfaces, including shock-bubble interactions, interface instability, impact and penetration processes, etc.

[0004] In recent years, physics-informed neural networks (PINNs) have provided a new paradigm for solving physical problems. They embed physical laws into the neural network training process and achieve efficient solutions to complex partial differential equations. They have been successfully applied to many fields such as incompressible flow, sonic flow and heat transfer problems. The development of PINNs has brought new opportunities for solving multi-media Riemann problems. Some researchers have proposed a learning-based FluxNets Riemann solver for the calculation of interface fluxes in the Godunov format, and studied transcritical / supercritical flows under non-ideal thermodynamic conditions. Others have proposed a physical constraint neural network model to solve the interface velocity of multi-media Riemann problems, and combined with the PGFM method to verify its application in compressible dual gas flows. Subsequently, some people proposed an unsupervised PCNN-RS method that does not require labeled data. It predicts the interface pressure and derives other interface states through a proxy model, and applies it to the GFM method to achieve multi-media interface evolution simulation. Based on this, how to accurately solve multi-media Riemann problems involving complex state equations to obtain accurate state predictions of multi-media fluid interactions has become one of the technical problems to be solved. Summary of the invention

[0005] In response to the problems existing in the above-mentioned traditional technologies, the present invention proposes a state prediction method for multi-media fluid interaction, a state prediction system for multi-media fluid interaction and a computer device, which can accurately solve the multi-media Riemann problem involving complex state equations and obtain accurate state prediction of multi-media fluid interaction.

[0006] In order to achieve the above objectives, the embodiments of the present invention adopt the following technical solutions: On the one hand, a method for predicting the state of multi-media fluid interaction is provided, comprising the steps of: The level set function is used to track and capture the position of the material interface of the multi-media fluid and calculate the interface normal vector; The continuation equation is used to perform the first normal continuation according to the interface normal vector; Construct a local multi-medium Riemann problem in the normal direction of the interface; The constructed multi-medium accurate Riemann solver is used to solve the local multi-medium Riemann problem and predict the output vector of the star region state solution of the local multi-medium Riemann problem. The star region state is the state after the interaction at the multi-medium interface. The input vector of the multi-medium accurate Riemann solver includes all the initial variables of the local multi-medium Riemann problem. The output vector of the multi-medium accurate Riemann solver includes the left-traveling wave velocity, the right-traveling wave velocity, the star region velocity, the star region pressure and the density on both sides of the contact discontinuity. The multi-medium accurate Riemann solver is a fully connected neural network architecture and uses the L-BFGS optimization strategy to minimize the set physical information loss function for optimization and solution. Perform a quadratic normal extension on the output vector of the multi-medium exact Riemann solver; After the quadratic normal extension, a high-order method is used to solve the control equations in space and time. The fourth-order WENO reconstruction is used for spatial calculation and the third-order TVD Runge-Kutta format is used for time advancement. The multi-media interface is advanced according to the calculated flow field results and periodically reinitialized to maintain the signed distance characteristics; Return to the above steps of using the level set function to track and capture the position of the material interface of the multi-media fluid and calculate the interface normal vector, execute iteratively until the final simulation time, and output the numerical simulation results of the multi-media fluid interaction.

[0007] On the other hand, a state prediction system for multi-media fluid interaction is also provided, comprising: An interface calculation module is used to track and capture the position of the material interface of the multi-media fluid using a level set function and calculate the interface normal vector; A first extension module, used for performing first normal extension according to the interface normal vector using the extension equation; Riemann construction module, used to construct local multi-medium Riemann problems in the normal direction of the interface; The solution prediction module is used to solve the local multi-media Riemann problem by using the constructed multi-media accurate Riemann solver, and predict the output vector of the star zone state solution of the local multi-media Riemann problem. The star zone state is the state after the interaction at the multi-media interface. The input vector of the multi-media accurate Riemann solver includes all the initial variables of the local multi-media Riemann problem. The output vector of the multi-media accurate Riemann solver includes the left-traveling wave velocity, the right-traveling wave velocity, the star zone velocity, the star zone pressure and the density on both sides of the contact discontinuity. The multi-media accurate Riemann solver is a fully connected neural network architecture and uses the L-BFGS optimization strategy to minimize the set physical information loss function for optimization and solution. The quadratic extension module is used to perform quadratic normal extension on the output vector of the multi-medium exact Riemann solver; The flow field advancement module is used to solve the control equations in space and time by using high-order methods; among them, the fourth-order WENO reconstruction is used for spatial calculation and the third-order TVD Runge-Kutta format is used for time advancement; The interface update module is used to advance the multi-media interface according to the flow field results calculated by the time-space discrete solution, and perform periodic reinitialization to maintain the signed distance characteristics; The iterative output module is used to jump to the above interface calculation module, execute iteratively until the final simulation time, and output the numerical simulation results of multi-media fluid interaction.

[0008] On the other hand, a computer device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the state prediction method for multi-media fluid interaction when executing the computer program.

[0009] One of the above technical solutions has the following advantages and beneficial effects: The above-mentioned state prediction system, method and equipment for multi-media fluid interaction completes deep learning modeling under physical constraints by embedding the control equations and constraints of the multi-media Riemann solution into the loss function and structure of the neural network, and realizes a multi-media precise Riemann solver based on PINNs. It learns the mapping relationship between input variables and output variables through physical information neural network training, and makes the output results strictly abide by the physical constraints specified by the Riemann problem, reduces the spatial dimension of the solution and accelerates convergence. Finally, under the Euler framework, it realizes the numerical simulation of multi-media interaction of complex engineering cases, can stably and accurately solve the multi-media Riemann problem, and predict the state after multi-media interaction. The prediction accuracy is higher and it is suitable for media with complex state equations. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the conventional technology, the drawings required for use in the embodiments or the conventional technology descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0011] Figure 1 A schematic flow chart of a method for predicting a state of a multi-media fluid interaction in one embodiment; Figure 2 A schematic diagram of a calculation process of multi-media interaction under an Euler framework in one embodiment; Figure 3 is a schematic diagram of a wave system structure in a multi-medium Riemann problem in one embodiment, Figure 3 (a) is the entropy condition, Figure 3 (b) is the shock wave entropy increase, Figure 3 (c) is the sparse wave solution, Figure 3 (d) is the contact discontinuity condition; Figure 4 A schematic diagram of a computational framework of a multi-medium exact Riemann solver in one embodiment; Figure 5 A block diagram of a multi-media fluid interaction state prediction system in one embodiment. DETAILED DESCRIPTION

[0012] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings and Examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art of the present invention. The terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0013] It should be noted that the reference to "embodiment" in this article means that the specific features, structures or characteristics described in conjunction with the embodiment may be included in at least one embodiment of the present invention. The presentation of this phrase at various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It will be appreciated by those skilled in the art that the embodiments described herein may be combined with other embodiments. The term "and / or" used in the specification and appended claims of the present invention refers to any combination of one or more of the associated listed items and all possible combinations, and includes these combinations.

[0014] The implementation modes of the present invention will be described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0015] Traditional Riemann solvers face significant challenges in solving multi-media Riemann problems. Their theoretical calculations require special analysis and derivation for different situations, and they cannot effectively solve problems involving complex state equations or physical mechanisms. Approximate Riemann solvers simplify the problem and improve the efficiency of the solution at the expense of accuracy. However, their low accuracy affects the computational error of the overall simulation. The core goal of the exact Riemann solver is to provide effective physical constraints for multi-media coupled systems, but its solution process often requires multiple iterations, is inefficient, time-consuming, and may fail due to divergence, making it difficult to solve.

[0016] However, the existing research on Riemann solvers based on PINNs is only for simple EOS (equations of state) such as gases, and is not applicable to complex EOS such as liquids. In addition, the proxy model relies on real solutions / numerical solutions, or random sampling training, which limits its practical application. In addition, model errors may accumulate and propagate to the solution of the problem, and the accuracy and stability of solving complex problems still need to be improved.

[0017] In one embodiment, Figure 1 As shown, a state prediction method for multi-media fluid interaction is provided, which may include the following steps S10 to S24: S10, using the level set function to track and capture the material interface position of the multi-media fluid and calculate the interface normal vector; S12, using the continuation equation to perform the first normal continuation according to the interface normal vector; S14, constructing a local multi-medium Riemann problem in the normal direction of the interface; S16, using the constructed multi-medium accurate Riemann solver to solve the local multi-medium Riemann problem, predicting the output vector of the star region state solution of the local multi-medium Riemann problem, where the star region state is the state after the interaction at the multi-medium interface; the input vector of the multi-medium accurate Riemann solver includes all the initial variables of the local multi-medium Riemann problem, and the output vector of the multi-medium accurate Riemann solver includes the left-traveling wave velocity, the right-traveling wave velocity, the star region velocity, the star region pressure and the density on both sides of the contact discontinuity. The multi-medium accurate Riemann solver is a fully connected neural network architecture and uses the L-BFGS optimization strategy to minimize the set physical information loss function for optimization and solution; S18, performing a secondary normal extension on the output vector of the multi-medium exact Riemann solver; S20, after the quadratic normal extension, a high-order method is used to solve the control equations in space and time. Among them, the fourth-order WENO reconstruction is used for spatial calculation and the third-order TVD Runge-Kutta format is used for time advancement. S22, advancing the multi-media interface according to the flow field results calculated by the time-space discrete solution, and performing periodic reinitialization to maintain the signed distance characteristics; S24, returning to the above step S10, looping and iterating (the above steps S10 to S22) until the final simulation time, and outputting the numerical simulation results of the multi-media fluid interaction.

[0018] Understandably, Figure 2 The calculation process of multi-media interaction under the Euler framework is demonstrated. This method combines the improved virtual fluid method (MGFM) with PINN-MERS (PINNs-based Multi-material Exact Riemann Solver), in which the interface capture adopts the level set method, the spatial discretization uses the fourth-order WENO (Weighted Essentially Non-Oscillatory) format, and the time discretization uses the third-order TVD (Total Variation Diminishing) Runge-Kutta format.

[0019] The calculation process for each time step includes the following key steps: Step 1: Interface identification. Using the level set function Tracking the location of material interfaces , interface normal vector pass Calculated, The interface capture method is realized by implicitly tracking the evolution of the material interface, which plays a key role in multi-media numerical simulation without explicit surface reconstruction.

[0020] Specifically, the level set method is used to represent and track the material interface. Represented as a high-dimensional scalar function The zero isosurface of is the spatial dimension, t Indicates time, Represents spatial coordinates.

[0021] The evolution of the level set function follows the transport equation: ; in, is the convection velocity. Signed distance characteristic ( ) facilitates accurate calculation of interface geometry, including normal vectors and curvature .

[0022] To maintain numerical stability and preserve the signed distance property during transport, the pseudo-time evolution equation is solved through a reinitialization process: ; in, is pseudo time, represents the initial level set function before reinitialization.

[0023] Step 2: First normal extension. Based on the implementation of the virtual fluid method, the multi-medium problem is decoupled and converted into multiple single-medium problems. Normal extension extends the interface state to adjacent virtual nodes, and the extension equation is: ; in, represents the physical quantity to be extrapolated, is the interface normal vector obtained by the level set method. The spatial derivative and time derivative are calculated using the first-order upwind scheme and forward Euler scheme, respectively.

[0024] Step 3: Update the interface state. Construct a local multi-medium Riemann problem in the normal direction of the interface. For each dielectric material, the state on the left corresponds to the real node near the interface, and the state on the right originates from the extrapolated value of the corresponding virtual node in step 2.

[0025] All the initial primitive variables of the constructed Riemann problem constitute the input vector of the multi-medium exact Riemann solver (PINN-MERS). After training and optimization through the physical loss function, the network predicts the output vector of the state solution of the star region of the Riemann problem. , and The virtual node states after multi-media interface interaction are defined to establish boundary conditions for single-media problems.

[0026] Step 4: Secondary normal extension and flow field advancement. The Riemann solution obtained in step 3 is subjected to secondary normal extension to fill the remaining virtual nodes. After secondary normal extension, a high-order method is used to solve the control equations in space and time, preferably using a fourth-order WENO reconstruction for spatial calculation and a third-order TVD Runge-Kutta format for time advancement.

[0027] Step 5: Interface update and reinitialization: The multi-media interface is advanced according to the calculated flow field results, and periodically reinitialized to maintain the signed distance characteristics.

[0028] The above five-step process is iterated until the final simulation time is reached.

[0029] The above-mentioned state prediction method of multi-media fluid interaction completes deep learning modeling under physical constraints by embedding the control equations and constraints of the multi-media Riemann solution into the loss function and structure of the neural network, realizes a multi-media precise Riemann solver based on PINNs, and learns the mapping relationship between input variables and output variables through physical information neural network training, and makes the output results strictly abide by the physical constraints stipulated by the Riemann problem, reduces the spatial dimension of the solution and accelerates convergence. Finally, under the Euler framework, the numerical simulation of multi-media interaction of complex engineering cases is realized, which can stably and accurately solve the multi-media Riemann problem and predict the state after multi-media interaction. The prediction accuracy is higher and it is suitable for media with complex state equations.

[0030] More specifically, the Euler equations are a set of hyperbolic partial differential equations that describe the motion of inviscid fluids, derived from the laws of conservation of mass, momentum, and energy. Its n-dimensional form can be expressed as: ; Among them, the conserved variable vector U Defined as: ; in, is the density, is the velocity vector, E is the total energy. The corresponding flux tensor The expression is: ; Here p For pressure, is the identity matrix. The tensor product (outer product) represents the product of two vectors to generate a second-order tensor. Total energy E satisfy: ; in, e Represents internal energy.

[0031] The material model includes the calculation of the equation of state (EOS) and the speed of sound, which are key to closing the Euler equations and determining the fluid behavior.

[0032] pressure p Through the equation of state and internal energy e and density Related: ; Speed ​​of sound in fluid c It is an important physical property parameter that can be derived from the state equation, characterizing the propagation rate of small pressure disturbances in the medium: ; where the partial derivative is at constant entropy s Obtained under conditions.

[0033] For an ideal gas, it satisfies: ; in is the adiabatic index (ratio of specific heats).

[0034] For rapid expanders, the Jones-Wilkins-Lee (JWL) equation of state is used: ; In the formula is the specific volume, A , B , R 1 , R 2 and is the material constant, is the initial density, e For internal energy.

[0035] The multi-medium Riemann problem in the Euler framework is defined by the discontinuous initial state: ; in, and Represent the left and right initial states respectively.

[0036] Figure 3 The typical wave structure including shock wave, rarefaction wave and contact discontinuity is shown. The solution of the Riemann problem of shock wave-rarefaction wave interaction is determined by the entropy condition as Figure 3 (a), where the Lax entropy condition is used to verify the physical acceptability of the shock wave: for a velocity S The propagating shock wave has characteristic velocities on both sides Must meet: ; here and They represent the characteristic velocities of the wave front and wave back states respectively. For rarefaction waves, the characteristic velocity must change monotonically within the wave system, that is, satisfy .

[0037] The initial state determines the specific wave system configuration. The combination of left and right wave types can produce four situations: left-moving shock wave and right-moving shock wave (SS), left-moving shock wave and right-moving rarefaction wave (SR), left-moving rarefaction wave and right-moving shock wave (RS), and left-moving rarefaction wave and right-moving rarefaction wave (RR). This manual excludes the vacuum formation situation caused by the lack of contact discontinuity leading to the separation of matter.

[0038] Shock wave conditions. Figure 3 As shown in (b), the shock wave satisfies the Rankine-Hugoniot jump condition: ; in, and is the conserved variable vector on both sides of the shock wave, F is the corresponding flux vector, S is the shock wave propagation speed.

[0039] Rarefaction wave conditions. Rarefaction waves are governed by characteristic compatibility conditions, and their self-similar solutions along the characteristic directions are determined by ordinary differential equations: ; in, is the original variable, and its upper right subscript indicates transposition. Corresponding characteristic speed The characteristic vector of is the characteristic velocity gradient. For the Euler equations, its components are explicitly expressed as: ; like Figure 3 (c) shows that the equation is changed from the initial state along the characteristic direction Integrate to intermediate state , we can get the sparse wave solution: ; The integration domain starts from the initial characteristic velocity Extend to end characteristic velocity .

[0040] Contact discontinuity conditions. Figure 3 As shown in (d), the pressure and velocity are continuous at the contact discontinuity, while the density is discontinuous: .

[0041] Regarding the above-mentioned PINNs-based Multi-medium Exact Riemann Solver (PINN-MERS): Physical Information Neural Networks (PINNs) achieve deep learning modeling under physical constraints by embedding the control equations into the loss function of the neural network. This specification proposes a PINNs-based Multi-medium Exact Riemann Solver (PINN-MERS) for solving multi-medium Riemann problems.

[0042] like Figure 4 As shown in Figure 1, the computational framework of PINN-MERS consists of three core components: network architecture, hard physical constraints, and physical information loss function construction. The wave system structure is determined by entropy conditions, and then the loss function for model parameter optimization is determined. This framework incorporates the physical constraints of the Riemann problem into the neural network, realizing the accurate solution of multi-medium Riemann under complex state equations.

[0043] Network architecture: A neural network can be viewed as a nonlinear mapping from an n-dimensional input space to an m-dimensional output space. Its mathematical expression is: ; in, Represents network parameters. Using a fully connected neural network architecture, for an L-layer network (including input / output layers): ; Weight Matrix and the bias vector Define the inter-layer transformation, Indicates The number of neurons in the layer. The hidden layer uniformly uses the hyperbolic tangent activation function .

[0044] For the multi-medium Riemann problem, the input vector combines the left and right initial primitive variables: ; in, represents the density, velocity and pressure of the left initial state, represents the density, velocity, and pressure in the initial state.

[0045] The star zone variables must meet the contact discontinuity conditions: ; The corresponding output vector is defined as: ; in, and denote the velocities of the left-traveling and right-traveling waves, respectively. and is the star region speed and pressure, and Represents the density on both sides of the contact discontinuity.

[0046] In one embodiment, the hard constraints of the multi-medium exact Riemann solver are introduced as follows: The implementation of hard constraints in the multi-medium exact Riemann solver PINN-MERS is designed to meet two key requirements: maintaining physical consistency to eliminate non-physical solutions caused by model bias, and strictly satisfying strong physical constraints that cannot be fully restricted by the penalty term of the loss function alone. This constraint implementation strategy reduces the optimization complexity by reducing the effective degrees of freedom of the model, while alleviating the multi-objective conflict in the loss function, thereby accelerating convergence and enhancing the robustness of the solution to the Riemann problem.

[0047] Specifically, in the multi-medium Riemann problem, the physical constraints are derived from interface conditions and thermodynamic admissibility. The conditions of pressure and velocity continuity at contact discontinuities are enforced by sharing output vector elements. Wave propagation requires strict adherence to velocity ordering. and positivity constraints ( , and ). The constraint enforcement strategy combines: ; in, represents the star region speed, Indicates the pressure of the star region, represents the left-traveling wave velocity, represents the right-traveling wave velocity, and represents the density on both sides of the contact discontinuity, is a smooth and strictly positive activation function.

[0048] Speed ​​constraints are implemented via chained transformations: Intermediate speed Constructed as Plus the positive offset caused by Softplus activation, and It is then defined as Add another positive offset generated by Softplus. This cascade structure guarantees strict inequality through monotonic function combination Thermodynamic variables are treated similarly, pressure ,density and Each of them is transformed with independent Softplus to ensure positivity. The complete constraint enforcement mechanism maintains the differentiability of gradient-based optimization while strictly adhering to the constraints determined by the physical laws of the Riemann problem.

[0049] In one embodiment, regarding the setting of physical information loss function of the multi-media exact Riemann solver: As a pure unsupervised learning framework, the loss function of the multi-media exact Riemann solver PINN-MERS is completely derived from the physical constraints derived from the governing equations of the Riemann problem.

[0050] Specifically, the wave structure of the solution is determined by the initial state, resulting in four left / right wave combinations: shock wave-shock wave (SS), shock wave-sparse wave (SR), sparse wave-shock wave (RS), and sparse wave-sparse wave (RR). Each combination requires specific physical constraints in the loss function, and the wave type is determined by entropy condition analysis before each training iteration.

[0051] The physical information loss function is set to be a composite loss function that combines the left / right wave contributions by operating condition dependency: ; Among them, SS combination represents shock wave-shock wave combination, SR combination represents shock wave-rarefaction wave combination, RS combination represents rarefaction wave-shock wave combination, and RR combination represents rarefaction wave-rarefaction wave combination. represents the shock wave loss of the left wave, represents the rarefaction loss of the left wave, represents the shock wave loss of the right wave, Represents the rarefaction wave loss of the right wave. is a binary weighting coefficient used to activate the corresponding wave pair combination.

[0052] Among them, for the shock wave that satisfies the Rankine-Hugoniot condition, the loss term is defined as: ; in, N is the number of initial condition sets, Indicates The shock wave velocity of the sample.

[0053] For the rarefaction wave controlled by the integral form, the loss term is constructed as: ; The path integral is numerically approximated using the fourth-order Runge-Kutta method with an integration step size of , where is determined empirically It can better balance calculation accuracy and efficiency.

[0054] The training process is to minimize the physical information loss function in the absence of labeled data, adopt the L-BFGS optimization strategy, and update the network parameters by back-propagation to calculate the gradient.

[0055] Regarding the above step S18, its numerical discretization format is specifically as follows: the finite difference method is used to solve the basic control equation (Euler equation), specifically using the fourth-order WENO format for spatial discretization and the third-order TVD Runge-Kutta format for time advancement.

[0056] The specific implementation is as follows: ; in, Acts on conserved variables U The space discretization operator.

[0057] The fourth-order WENO format reconstructs the unit interface flux through a convex combination of low-order polynomials. The combination weight is determined based on the smoothness of each template solution, and a smaller weight is given to the template containing discontinuities. In one dimension, the spatial discretization operator of the fourth-order WENO format is It can be expressed as: ; in, and is the numerical flux of the unit interface, calculated by WENO reconstruction.

[0058] To ensure numerical stability, the time step Controlled by CFL conditions: ; in, is the spatial step length, is the velocity vector, is the speed of sound, is the Courant number (usually less than 1), and the maximum value is calculated at all grid points to ensure that the conditions are met globally.

[0059] The above prediction scheme embeds the control equations and constraints of the multi-media Riemann solver into the loss function and structure of the neural network to complete the deep learning modeling under physical constraints and realize the PINNs-based multi-media accurate Riemann solver (PINN-MERS). Input the original variable value of the initial state , output the variable value of the star zone status The essence of the multi-media accurate Riemann solver is to learn the mapping relationship between input variables and output variables through physical information neural network training. By introducing hard constraints in the neural network, the output results strictly comply with the physical constraints specified by the Riemann problem, reducing the spatial dimension of the solution and accelerating convergence. Under the Euler framework, by combining the improved virtual fluid method (MGFM) with PINN-MERS, accurate numerical simulation of multi-media interactions in complex engineering cases is achieved.

[0060] The above-mentioned multi-medium precise Riemann solver can stably and accurately solve the multi-medium Riemann problem and predict the state after the multi-medium interaction. Compared with the traditional approximate Riemann solver, the multi-medium precise Riemann solver proposed in this specification has higher accuracy and is more stable. It will not fail to converge and can always give a relatively accurate prediction result output, which is suitable for media with complex state equations.

[0061] In some embodiments, in order to verify the effectiveness of the above-mentioned method, this experimental example uses a one-dimensional shock tube problem to conduct an experiment. The experiment involves a variety of media, including gas and rapid expansion, where the material model parameters corresponding to different media are as follows: Gas 1 takes , gas 2 takes , rapid expansion , , , , , .

[0062] Four cases were set up in the experiment. The corresponding left and right media and the values ​​of the initial original variables are shown in Table 1. The units of density, velocity, and pressure are . TC1 and TC2 have the same medium on the left and right, and by setting different initial conditions, the corresponding wave system structures are RR and SS respectively. TC3 and TC4 have different media on the left and right sides. Table 2 shows the calculation results and error comparison between the traditional approximate Riemann solver HLLC and the PINN-MERS of the present invention. It can be seen that the calculation results of PINN-MERS have smaller errors and higher accuracy. As the state equation becomes more and more complex, the error becomes larger and larger, but the accuracy is always higher than that of the traditional approximate Riemann solver HLLC.

[0063] Table 1

[0064] Table 2

[0065] It should be understood that although the above process Figure 1 The steps in the flowchart are shown in the order indicated by the arrows, but the steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of the steps, and the steps can be executed in other orders. Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequentially, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0066] In one embodiment, Figure 5As shown, a state prediction system 100 for multi-media fluid interaction is provided, comprising an interface calculation module 11, a first extension module 13, a Riemann construction module 15, a solution prediction module 17, a second extension module 19, a flow field advancement module 21, an interface update module 23 and an iterative output module 25. Among them, the interface calculation module 11 is used to track and capture the material interface position of the multi-media fluid using a level set function and calculate the interface normal vector. The first extension module 13 is used to perform the first normal extension according to the interface normal vector using the extension equation. The Riemann construction module 15 is used to construct a local multi-media Riemann problem in the interface normal direction. The solution prediction module 17 is used to solve the local multi-media Riemann problem by using the constructed multi-media accurate Riemann solver, and predict the output vector of the star zone state solution of the local multi-media Riemann problem. The star zone state is the state after the interaction at the multi-media interface; the input vector of the multi-media accurate Riemann solver includes all the initial variables of the local multi-media Riemann problem, and the output vector of the multi-media accurate Riemann solver includes the left-traveling wave velocity, the right-traveling wave velocity, the star zone velocity, the star zone pressure and the density on both sides of the contact discontinuity. The multi-media accurate Riemann solver is a fully connected neural network architecture and uses the L-BFGS optimization strategy to minimize the set physical information loss function for optimization and solution. The secondary extension module 19 is used to perform secondary normal extension on the output vector of the multi-media accurate Riemann solver; the flow field advancement module 21 is used to use a high-order method to perform time-space discrete solutions to the control equations; among them, the fourth-order WENO reconstruction is used for spatial calculation and the third-order TVD Runge-Kutta format is used for time advancement. The interface update module 23 is used to advance the multi-media interface according to the flow field results calculated by the time-space discrete solution, and perform periodic reinitialization to maintain the signed distance characteristics. The iterative output module 25 is used to jump to the interface calculation module, iteratively execute until the final simulation time, and output the multi-media fluid interaction numerical simulation results.

[0067] The above-mentioned state prediction system 100 of multi-media fluid interaction completes deep learning modeling under physical constraints by embedding the control equations and constraints of the multi-media Riemann solution into the loss function and structure of the neural network, and realizes a multi-media precise Riemann solver based on PINNs. It learns the mapping relationship between input variables and output variables through physical information neural network training, and makes the output results strictly abide by the physical constraints stipulated by the Riemann problem, reduces the spatial dimension of the solution and accelerates convergence. Finally, under the Euler framework, it realizes the numerical simulation of multi-media interaction of complex engineering cases, can stably and accurately solve the multi-media Riemann problem, and predict the state after multi-media interaction. The prediction accuracy is higher and it is suitable for media with complex state equations.

[0068] In one embodiment, the hard constraints of the multi-medium exact Riemann solver include: ; in, represents the star region speed, Indicates the pressure of the star region, represents the left-traveling wave velocity, represents the right-traveling wave velocity, and represents the density on both sides of the contact discontinuity, and Softplus(·) is a smooth and strictly positive activation function.

[0069] In one embodiment, the set physical information loss function of the multi-medium exact Riemann solver is: ; Among them, SS combination represents shock wave-shock wave combination, SR combination represents shock wave-rarefaction wave combination, RS combination represents rarefaction wave-shock wave combination, and RR combination represents rarefaction wave-rarefaction wave combination. represents the shock wave loss of the left wave, represents the rarefaction loss of the left wave, represents the shock wave loss of the right wave, represents the rarefaction loss of the right wave, is the binary weighting coefficient.

[0070] For the specific limitations of the multi-media fluid interaction state prediction system 100 , please refer to the corresponding limitations of the multi-media fluid interaction state prediction method mentioned above, which will not be repeated here.

[0071] In one embodiment, a computer device is also provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the following processing steps are implemented: using a level set function to track and capture the material interface position of the multi-media fluid and calculate the interface normal vector; using an extension equation to perform a first normal extension according to the interface normal vector; constructing a local multi-media Riemann problem in the interface normal direction; using the constructed multi-media precise Riemann solver to solve the local multi-media Riemann problem, predicting the output vector of the star region state solution of the local multi-media Riemann problem, the star region state being the state after interaction at the multi-media interface; the input vector of the multi-media precise Riemann solver includes all initial variables of the local multi-media Riemann problem, and the output vector of the multi-media precise Riemann solver includes the left-traveling wave velocity, the right-traveling wave velocity The multi-medium precise Riemann solver is a fully connected neural network architecture and uses the L-BFGS optimization strategy to minimize the set physical information loss function for optimization and solution; the output vector of the multi-medium precise Riemann solver is subjected to quadratic normal extension; after the quadratic normal extension, a high-order method is used to perform spatiotemporal discrete solutions to the control equations; among them, the fourth-order WENO reconstruction is used for spatial calculation and the third-order TVD Runge-Kutta format is used for time advancement; the multi-medium interface is advanced according to the calculated flow field results, and periodic reinitialization is performed to maintain the signed distance characteristics; the above-mentioned steps of using the level set function to track and capture the material interface position of the multi-medium fluid and calculate the interface normal vector are returned, and the loop is iterated until the final simulation time, and the numerical simulation results of the multi-medium fluid interaction are output.

[0072] In one embodiment, when the processor executes the computer program, the processor can also implement the processing steps of the state prediction method of the multimedia fluid interaction in other embodiments described above.

[0073] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus dynamic random access memory (RambusDRAM, referred to as RDRAM) and interface dynamic random access memory (DRDRAM).

[0074] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0075] The above embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of protection of the invention. It should be pointed out that, for those of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the attached claims.

Claims

1. A state prediction method for multi-media fluid interaction, characterized in that: Includes steps: The level set function is used to track and capture the position of the material interface of the multi-media fluid and calculate the interface normal vector; Using the continuation equation to perform the first normal continuation according to the interface normal vector; Construct a local multi-medium Riemann problem in the normal direction of the interface; The local multi-medium Riemann problem is solved by using the constructed multi-medium exact Riemann solver, and the output vector of the star region state solution of the local multi-medium Riemann problem is predicted, where the star region state is the state after the interaction at the multi-medium interface; The input vector of the multi-medium accurate Riemann solver includes all the initial variables of the local multi-medium Riemann problem, and the output vector of the multi-medium accurate Riemann solver includes the left-traveling wave velocity, the right-traveling wave velocity, the star region velocity, the star region pressure and the density on both sides of the contact discontinuity. The multi-medium accurate Riemann solver is a fully connected neural network architecture and uses the L-BFGS optimization strategy to minimize the set physical information loss function for optimization and solution; Performing a secondary normal extension on the output vector of the multi-medium exact Riemann solver; After the quadratic normal extension, a high-order method is used to solve the control equations in space and time. The fourth-order WENO reconstruction is used for spatial calculation and the third-order TVD Runge-Kutta format is used for time advancement. The multi-media interface is advanced according to the flow field results calculated by the time-space discrete solution, and periodically reinitialized to maintain the signed distance characteristics; Return to the step of using the level set function to track and capture the position of the material interface of the multi-media fluid and calculate the interface normal vector, and iterate the loop until the final simulation time, and output the multi-media fluid interaction numerical simulation result.

2. The state prediction method of multimedia fluid interaction according to claim 1, characterized in that: The hard constraints of the multi-medium exact Riemann solver include: in, represents the star region speed, Indicates the pressure of the star region, represents the left-traveling wave velocity, represents the right-traveling wave velocity, and represents the density on both sides of the contact discontinuity, and Softplus(·) is a smooth and strictly positive activation function.

3. The state prediction method of multimedia fluid interaction according to claim 1 or 2, characterized in that: The set physical information loss function of the multi-medium exact Riemann solver is: Among them, SS combination represents shock wave-shock wave combination, SR combination represents shock wave-rarefaction wave combination, RS combination represents rarefaction wave-shock wave combination, and RR combination represents rarefaction wave-rarefaction wave combination. represents the shock wave loss of the left wave, represents the rarefaction loss of the left wave, represents the shock wave loss of the right wave, represents the rarefaction loss of the right wave, is the binary weighting coefficient.

4. A state prediction system for multi-media fluid interaction, characterized in that: include: An interface calculation module is used to track and capture the position of the material interface of the multi-media fluid using a level set function and calculate the interface normal vector; A first continuation module, used for performing first normal continuation according to the interface normal vector by using a continuation equation; Riemann construction module, used to construct local multi-medium Riemann problems in the normal direction of the interface; A solution prediction module is used to solve the local multi-medium Riemann problem by using the constructed multi-medium exact Riemann solver, and predict the output vector of the star region state solution of the local multi-medium Riemann problem, where the star region state is the state after the interaction at the multi-medium interface; The input vector of the multi-medium accurate Riemann solver includes all the initial variables of the local multi-medium Riemann problem, and the output vector of the multi-medium accurate Riemann solver includes the left-traveling wave velocity, the right-traveling wave velocity, the star region velocity, the star region pressure and the density on both sides of the contact discontinuity. The multi-medium accurate Riemann solver is a fully connected neural network architecture and uses the L-BFGS optimization strategy to minimize the set physical information loss function for optimization and solution; A secondary extension module, used for performing secondary normal extension on the output vector of the multi-medium accurate Riemann solver; The flow field advancement module is used to solve the control equations in space and time by using high-order methods; among them, the fourth-order WENO reconstruction is used for spatial calculation and the third-order TVD Runge-Kutta format is used for time advancement; The interface update module is used to advance the multi-media interface according to the flow field results calculated by the time-space discrete solution, and perform periodic reinitialization to maintain the signed distance characteristics; The iterative output module is used to jump to the interface calculation module, execute iteratively in a loop until the final simulation time, and output the numerical simulation results of the multi-media fluid interaction.

5. The state prediction system of multimedia fluid interaction according to claim 4, characterized in that: The hard constraints of the multi-medium exact Riemann solver include: in, represents the star region speed, Indicates the pressure of the star region, represents the left-traveling wave velocity, represents the right-traveling wave velocity, and represents the density on both sides of the contact discontinuity, and Softplus(·) is a smooth and strictly positive activation function.

6. The state prediction system of multimedia fluid interaction according to claim 4 or 5, characterized in that: The set physical information loss function of the multi-medium exact Riemann solver is: Among them, SS combination represents shock wave-shock wave combination, SR combination represents shock wave-rarefaction wave combination, RS combination represents rarefaction wave-shock wave combination, and RR combination represents rarefaction wave-rarefaction wave combination. represents the shock wave loss of the left wave, represents the rarefaction loss of the left wave, represents the shock wave loss of the right wave, represents the rarefaction loss of the right wave, is the binary weighting coefficient.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method for predicting the state of multimedia fluid interaction according to any one of claims 1 to 3 are implemented.

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