State Prediction System, Method and Equipment for Multi-Medium Fluid Interaction

Abstract

The present invention relates to a state prediction system, method and device for multi-medium fluid interaction. By embedding the control equations and constraint conditions of multi-medium Riemann solving into the loss function and structure of a neural network, deep learning modeling under physical constraints is completed, and an accurate multi-medium Riemann solver based on PINNs is realized, so as to learn the mapping relationship between input variables and output variables through training of a physics-informed neural network, and make the output results strictly comply with the physical constraints specified by the Riemann problem, reduce the dimensionality of the solution space and accelerate convergence. Finally, in the Euler framework, numerical simulation of multi-medium interaction in complex engineering cases is realized, which can stably and accurately solve multi-medium Riemann problems, predict the state after multi-medium interaction, with higher prediction accuracy and applicable to media with complex equations of state.

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 the interaction of multi-media fluids. Background Art

[0002] In the field of high-speed transient hydrodynamics, especially in complex non-equilibrium flows such as shock wave propagation and interfacial instability evolution under extreme loadings, the research on 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 media interface, which directly restricts the development of interfacial instability and the evolution of the multiphase flow field. Research shows that the multi-media Riemann solver based on the hyperbolic conservation law system can effectively improve the numerical fidelity of the mass, momentum, and energy transport processes across the media boundary by accurately depicting the coupling mechanism at the interface.

[0003] The multi-media Riemann solver is often combined with numerical methods to construct an interface model, which can be used to calculate the numerical flux of the material interface or directly define the interface conditions in the virtual fluid method (i.e., Ghost Fluid Method, GFM). GFM-based methods based on Riemann solutions (such as the Modified GFM (MGFM), Real GFM (RGFM), and Practical GFM (PGFM)) have strong robustness and are suitable for challenging problem scenarios such as large contact discontinuities and strong pressure jumps at the interface, including scenarios such as shock-bubble interaction, interfacial instability, shock, and penetration processes.

[0004] In recent years, Physics-Informed Neural Networks (PINNs) have provided a new paradigm for solving physical problems. By embedding physical laws into the neural network training process, they have achieved the efficient solution of complex partial differential equations and have been successfully applied to multiple 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 calculating the interface flux in the Godunov format and studied trans-critical / super-critical flows under non-ideal thermodynamic states. Others have proposed a physical-constrained neural network model to solve the interface velocity of multi-media Riemann problems and verified its application in compressible two-gas flows in combination with the PGFM method. Subsequently, an unsupervised PCNN-RS method without labeled data has been proposed, which predicts the interface pressure through a surrogate model and derives other interface states, and is applied to GFM-based methods to realize the simulation of multi-media interface evolution. Based on this, how to accurately solve multi-media Riemann problems involving complex equations of state 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 view of the problems existing in the above-mentioned traditional technologies, the present invention proposes a method for predicting the state of multi-medium fluid interaction, a system for predicting the state of multi-medium fluid interaction, and a computer device, which can accurately solve the multi-medium Riemann problem involving complex state equations and obtain an accurate state prediction of multi-medium fluid interaction.

[0006] To achieve the above object, the embodiments of the present invention adopt the following technical solutions:

[0007] On the one hand, a method for predicting the state of multi-medium fluid interaction is provided, including the steps of:

[0008] Using a level set function to track and capture the position of the material interface of the multi-medium fluid and calculating the interface normal vector;

[0009] Performing the first normal extension according to the interface normal vector by using the extension equation;

[0010] Constructing a local multi-medium Riemann problem in the interface normal direction;

[0011] 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, and the star region state is used as the state after the interaction at the multi-medium interface; the input vector of the multi-medium accurate Riemann solver includes all 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 densities 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;

[0012] Performing a second normal extension on the output vector of the multi-medium accurate Riemann solver;

[0013] After the second normal extension, using a high-order method to perform space-time discretization and solution of the control equation; among them, fourth-order WENO reconstruction is used for spatial calculation and third-order TVD Runge-Kutta format is used for time advancement;

[0014] Advancing the multi-medium interface according to the calculated flow field results and performing periodic re-initialization to maintain the signed distance property;

[0015] Return to the step of using the level set function to track and capture the position of the material interface of the multi-medium fluid and calculating the interface normal vector, and perform loop iteration until the final simulation time, and output the numerical simulation results of multi-medium fluid interaction.

[0016] On the other hand, a system for predicting the state of multi-medium fluid interaction is also provided, including:

[0017] The interface calculation module is used to track and capture the position of the material interface of the multi-medium fluid by using the level set function and calculate the interface normal vector;

[0018] The first extension module is used to perform the first normal extension according to the interface normal vector by using the extension equation;

[0019] The Riemann construction module is used to construct a local multi-medium Riemann problem in the interface normal direction;

[0020] The solution prediction module is used to solve the local multi-medium Riemann problem by using the constructed multi-medium exact Riemann solver, predict the output vector of the star region state solution of the local multi-medium Riemann problem, and the star region state is used as the state after the interaction at the multi-medium interface; the input vector of the multi-medium exact Riemann solver includes all the initial variables of the local multi-medium Riemann problem, and the output vector of the multi-medium exact Riemann solver includes the left-traveling wave velocity, the right-traveling wave velocity, the star region velocity, the star region pressure, and the densities on both sides of the contact discontinuity. The multi-medium exact Riemann solver is a fully connected neural network architecture and is optimized by using the L-BFGS optimization strategy to minimize the set physical information loss function;

[0021] The second extension module is used to perform the second normal extension on the output vector of the multi-medium exact Riemann solver;

[0022] The flow field advancement module is used to discretize and solve the governing equations in space and time by using a high-order method; among them, fourth-order WENO reconstruction is used for spatial calculation and third-order TVD Runge-Kutta format is used for time advancement;

[0023] The interface update module is used to advance the multi-medium interface according to the flow field results calculated by the space-time discrete solution and perform periodic re-initialization to maintain the signed distance property;

[0024] The iterative output module is used to jump to the above interface calculation module, loop and iterate until the final simulation time, and output the numerical simulation results of the multi-medium fluid interaction.

[0025] On the other hand, 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 steps of the above state prediction method for multi-medium fluid interaction are implemented.

[0026] One of the above technical solutions has the following advantages and beneficial effects:

[0027] The above-mentioned state prediction system, method and equipment for multi-media fluid interaction complete deep learning modeling under physical constraints by embedding the control equations and constraint conditions of multi-media Riemann solution into the loss function and structure of the neural network, realizing an accurate multi-media Riemann solver based on PINNs, so as to learn the mapping relationship between input variables and output variables through training of the physics-informed neural network, and make the output results strictly comply with the physical constraints specified by the Riemann problem, reduce the dimensionality of the solution space and accelerate convergence. Finally, in the Euler framework, numerical simulation of multi-media interaction in complex engineering cases is realized, the multi-media Riemann problem can be solved stably and accurately, the state after multi-media interaction can be predicted, and the prediction accuracy is higher and it is applicable to media with complex equations of state. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or in the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0029] Figure 1 It is a schematic flow chart of a state prediction method for multi-media fluid interaction in an embodiment;

[0030] Figure 2 It is a schematic diagram of the calculation process of multi-media interaction under the Euler framework in an embodiment;

[0031] Figure 3 It is a schematic diagram of the wave system structure in a multi-media Riemann problem in an embodiment, Figure 3 (a) is the entropy condition, Figure 3 (b) is the entropy increase of the shock wave, Figure 3 (c) is the rarefaction wave solution, Figure 3 (d) is the contact discontinuity condition;

[0032] Figure 4 It is a schematic diagram of the calculation framework of an accurate multi-media Riemann solver in an embodiment;

[0033] Figure 5 It is a block diagram of the modules of a state prediction system for multi-media fluid interaction in an embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] To make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs. The terms used in the description of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0035] It should be noted that referring to "embodiment" in this document means that a specific feature, structure or characteristic described in connection with the embodiment may be included in at least one embodiment of the present invention. The phrase is shown at various positions in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art can understand that the embodiments described herein can be combined with other embodiments. The term "and / or" used in the description and appended claims of the present invention refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0036] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0037] Traditional Riemann solvers face significant challenges when solving multi - medium Riemann problems. Their theoretical calculations require specialized analysis and derivation for different situations and cannot effectively solve problems when complex equations of state or physical mechanisms are involved. Approximate Riemann solvers improve the solution efficiency by simplifying the problem at the cost of sacrificing accuracy, which affects the computational error of the overall simulation due to low accuracy. The core objective of an exact Riemann solver is to provide effective physical constraints for a multi - medium coupling system, but its solution process often requires multiple iterations, with low efficiency, significant time consumption and may diverge and fail, making it difficult to solve.

[0038] Existing research on Riemann solvers based on PINNs only targets simple EOSs (equations of state) such as gases and is insufficient for complex EOSs such as liquids. Moreover, the surrogate model depends on true solutions / numerical solutions or random sampling training, limiting its practical application. In addition, model errors may accumulate and propagate to the solution of the problem, and the solution accuracy and stability of complex problems still need to be improved.

[0039] In one embodiment, as Figure 1 shown, a method for predicting the state of multi - medium fluid interaction is provided, which may include the following steps S10 to S24:

[0040] S10, using a level - set function to track and capture the position of the material interface of the multi - medium fluid and calculating the interface normal vector;

[0041] S12, perform the first normal extension according to the interface normal vector using the extension equation;

[0042] S14, construct a local multi - medium Riemann problem in the interface normal direction;

[0043] S16, use the constructed multi - medium exact Riemann solver to solve the local multi - medium Riemann problem, predict the output vector of the star region state solution of the local multi - medium Riemann problem, and the star region state is used as the state after interaction at the multi - medium interface; the input vector of the multi - medium exact Riemann solver includes all initial variables of the local multi - medium Riemann problem, and the output vector of the multi - medium exact Riemann solver includes the left - traveling wave velocity, right - traveling wave velocity, star region velocity, star region pressure, and densities on both sides of the contact discontinuity. The multi - medium exact Riemann solver is a fully - connected neural network architecture and is optimized using the L - BFGS optimization strategy to minimize the set physical information loss function;

[0044] S18, perform the second normal extension on the output vector of the multi - medium exact Riemann solver;

[0045] S20, after the second normal extension, use a high - order method to perform space - time discretization and solve the governing equations; specifically, use fourth - order WENO reconstruction for spatial calculation and third - order TVD Runge - Kutta format for time advancement;

[0046] S22, advance the multi - medium interface according to the flow field results after space - time discretization and solution, and perform periodic re - initialization to maintain the signed - distance property;

[0047] S24, return to the above step S10, and loop and iterate (the above steps S10 to S22) until the final simulation time, and output the numerical simulation results of multi - medium fluid interaction.

[0048] It can be understood that Figure 2 shows the calculation process of multi - medium interaction in the Eulerian framework. This method combines the improved ghost fluid method (MGFM) with PINN - MERS (PINNs - based Multi - material Exact Riemann Solver). The interface capturing uses 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.

[0049] The calculation process for each time step includes the following key steps:

[0050] Step 1: Interface recognition. The level set function is used to track the position of the material interface , and the interface normal vector is calculated through and obtained. is the material region. Among them, the interface capturing method is realized by implicitly tracking the evolution of the material interface and plays a key role in multi-medium numerical simulation without explicit surface reconstruction.

[0051] Specifically, the level set method is used to represent and track the material interface. This method represents the interface as the zero isosurface of a high-dimensional scalar function , where is the spatial dimension, t represents time, represents the spatial coordinates.

[0052] The evolution of the level set function follows the transport equation:

[0053] ;

[0054] where is the convective velocity. The signed distance property ( ) facilitates the accurate calculation of interface geometric quantities, including the normal vector and the curvature .

[0055] To maintain numerical stability and the signed distance property during the transport process, the pseudo-time evolution equation is solved through the reinitialization process:

[0056] ;

[0057] where is the pseudo-time, represents the initial level set function before reinitialization.

[0058] Step 2: First normal extension. The implementation based on the virtual fluid method decouples the multi-medium problem and transforms it into multiple single-medium problems. The normal extension extends the interface state to adjacent virtual nodes, and the extension equation is:

[0059] ;

[0060] where represents the physical quantity to be extrapolated, is the interface normal vector obtained by the level set method. The spatial derivative and the time derivative are calculated using the first-order upwind scheme and the forward Euler scheme respectively.

[0061] Step 3: Interface state update. Locally construct a multi - medium Riemann problem in the interface normal direction. For each medium material, the left - hand state corresponds to the real nodes near the interface, and the right - hand state is derived from the extrapolated values of the corresponding virtual nodes in Step 2.

[0062] The initial primitive variables of all constructed Riemann problems form 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 star - region state solution of the Riemann problem. The , and in the output vector define the virtual node state after multi - medium interface interaction, and establish boundary conditions for the single - medium problem.

[0063] Step 4: Second - order normal extension and flow - field advancement. Perform a second - order normal extension on the Riemann solution obtained in Step 3 to fill the remaining virtual nodes. After the second - order normal extension, use a high - order method to discretize and solve the governing equations in space and time. Preferably, use fourth - order WENO reconstruction for spatial calculation and third - order TVD Runge - Kutta format for time advancement.

[0064] Step 5: Interface update and re - initialization. Advance the multi - medium interface according to the calculated flow - field results and perform periodic re - initialization to maintain the signed - distance property.

[0065] The above five - step process is iteratively executed until the set final simulation time is reached.

[0066] The above - mentioned state prediction method for multi - medium fluid interaction embeds the governing equations and constraint conditions of multi - medium Riemann solving into the loss function and structure of the neural network, completes deep - learning modeling under physical constraints, realizes a multi - medium exact Riemann solver based on PINNs, learns the mapping relationship between input variables and output variables through training of the physics - informed neural network, and makes the output results strictly comply with the physical constraints specified by the Riemann problem, reduces the spatial dimension of the solution and speeds up convergence. Finally, in the Eulerian framework, it realizes the numerical simulation of multi - medium interaction in complex engineering cases, can stably and accurately solve the multi - medium Riemann problem, predict the state after multi - medium interaction, has higher prediction accuracy and is applicable to media with complex equations of state.

[0067] More specifically, the Euler equations are a system of hyperbolic partial differential equations describing the motion of inviscid fluids, originating from the laws of conservation of mass, momentum, and energy. Its n - dimensional form can be expressed as:

[0068] ;

[0069] where the conserved - variable vector U is defined as:

[0070] ;

[0071] wherein, is the density, is the velocity vector, E is the total energy. The corresponding flux tensor is expressed as:

[0072] ;

[0073] Here p is the pressure, is the identity matrix. is the tensor product (outer product), representing the product of two vectors to generate a second-order tensor. The total energy E satisfies:

[0074] ;

[0075] wherein, e represents the internal energy.

[0076] The material model includes the calculation of the equation of state (EOS) and the sound speed, which are the keys to closing the Euler equations and determining the fluid behavior.

[0077] The pressure p is related to the internal energy e and the density through the equation of state:

[0078] ;

[0079] The sound speed c in the fluid is an important physical property parameter that can be derived from the equation of state, characterizing the propagation rate of small pressure perturbations in the medium:

[0080] ;

[0081] where the partial derivative is obtained under the condition of constant entropy s .

[0082] For an ideal gas, it satisfies:

[0083] ;

[0084] where is the adiabatic index (specific heat ratio).

[0085] For a rapidly expanding material, the Jones-Wilkins-Lee (JWL) equation of state is adopted:

[0086] ;

[0087] In the formula is the specific volume, A , B , R 1, R 2, and are material constants, is the initial density, e is the internal energy.

[0088] The multi - medium Riemann problem in the Eulerian framework is defined by a discontinuous initial state:

[0089] ;

[0090] where, and represent the left and right initial states, respectively.

[0091] Figure 3 shows a typical wave system structure including shock waves, rarefaction waves, and contact discontinuities. The solution of the shock - rarefaction wave interaction in the Riemann problem is determined by the entropy condition as shown in Figure 3 (a), where the Lax entropy condition is used to verify the physical acceptability of the shock wave: for a shock wave propagating at velocity S , the characteristic velocities on both sides of it must satisfy:

[0092] ;

[0093] Here and represent the characteristic velocities of the states before and after the wave front, respectively. For a rarefaction wave, the characteristic velocity must vary monotonically within the wave system, that is, satisfy .

[0094] The initial state determines the specific wave system configuration. The combination of left - hand and right - hand wave types can produce four cases: left - moving shock wave and right - moving shock wave (S - S), left - moving shock wave and right - moving rarefaction wave (S - R), left - moving rarefaction wave and right - moving shock wave (R - S), left - moving rarefaction wave and right - moving rarefaction wave (R - R). This specification excludes the case of vacuum formation caused by the absence of contact discontinuities resulting in material separation.

[0095] Shock wave condition. As shown in Figure 3 (b), the shock wave satisfies the Rankine - Hugoniot jump condition:

[0096] ;

[0097] where, and are the vectors of conserved variables on both sides of the shock wave, F is the corresponding flux vector, S is the shock wave propagation velocity.

[0098] Rarefaction wave condition. The rarefaction wave is controlled by the characteristic compatibility condition, and its self-similar solution is determined by an ordinary differential equation along the characteristic direction:

[0099] ;

[0100] where is the original variable, and the superscript indicates the transpose, is the corresponding characteristic velocity of the characteristic vector, is the characteristic velocity gradient. For the Euler equations, its components are explicitly expressed as:

[0101] ;

[0102] As Figure 3 shown in (c), integrating the equation along the characteristic direction from the initial state to the intermediate state , the rarefaction wave solution can be obtained:

[0103] ;

[0104] The integration domain extends from the initial characteristic velocity to the termination characteristic velocity .

[0105] Contact discontinuity condition. As Figure 3 shown in (d), the pressure and velocity are continuous at the contact discontinuity, and the density shows a discontinuity:

[0106] .

[0107] Regarding the above-mentioned physics-informed neural network-based multi-medium exact Riemann solver (PINN-MERS): The physics-informed neural network (PINNs) realizes deep learning modeling under physical constraints by embedding the governing equations into the loss function of the neural network. This specification proposes a physics-informed neural network-based multi-medium exact Riemann solver (PINN-MERS) for solving multi-medium Riemann problems.

[0108] As Figure 4 shown, the computational framework of PINN-MERS includes three core components: network architecture, hard physical constraints, and construction of the physics-informed loss function. The wave system structure is determined by the entropy condition, and then the loss function for optimizing the model parameters is determined. This framework integrates the physical constraints of the Riemann problem into the neural network, realizing the accurate solution of multi-medium Riemann under complex equations of state.

[0109] Network architecture: The neural network can be regarded as a non-linear mapping from the n-dimensional input space to the m-dimensional output space, and its mathematical expression is:

[0110] ;

[0111] Among them, represents network parameters. Using a fully connected neural network architecture, for an L-layer network (including the input / output layer):

[0112] ;

[0113] weight matrix and bias vector define the transformation between layers, represents the number of neurons in the layer. The hidden layer uniformly adopts the hyperbolic tangent activation function

[0114] For the multi-medium Riemann problem, the input vector combines the left and right initial primitive variables:

[0115] ;

[0116] Among them, represents the density, velocity, and pressure of the left initial state, represents the density, velocity, and pressure of the right initial state.

[0117] The star region variables need to satisfy the contact discontinuity condition:

[0118] ;

[0119] The corresponding output vector is defined as:

[0120] ;

[0121] Among them, and represent the left-traveling wave and right-traveling wave velocities respectively, and are the star region velocity and pressure, and represent the densities on both sides of the contact discontinuity.

[0122] In one embodiment, the introduction of the hard constraint conditions for the multi-medium exact Riemann solver is as follows: The implementation of the hard constraint conditions in the multi-medium exact Riemann solver PINN-MERS aims to meet two key requirements: maintaining physical consistency to eliminate non-physical solutions caused by model biases, and strictly satisfying strong physical constraint conditions that cannot be fully restricted by only the penalty terms of the loss function. This constraint implementation strategy reduces the optimization complexity by reducing the effective degrees of freedom of the model, while alleviating the multi-objective conflicts in the loss function, thereby accelerating convergence and enhancing the robustness of the Riemann problem solution.

[0123] Specifically, in the multi - medium Riemann problem, physical constraints come from interface conditions and thermodynamic admissibility. The conditions of pressure and velocity continuity at the contact discontinuity are enforced by sharing output vector elements. Wave propagation requires strict adherence to velocity ordering and positivity constraints ( , and ). The constraint enforcement strategy combines:

[0124] ;

[0125] where represents the star region velocity, represents the star region pressure, represents the left - running wave velocity, represents the right - running wave velocity, and represent the densities on both sides of the contact discontinuity, is a smooth and strictly positive activation function.

[0126] The velocity constraint is enforced through a chain transformation: the intermediate velocity is constructed as plus a positive offset generated by the Softplus activation, while is subsequently defined as plus another positive offset generated by Softplus. This cascading structure ensures the strict inequality through the combination of monotonic functions. Similar treatment is applied to thermodynamic variables, and the pressure , density and are respectively passed through independent Softplus transforms to ensure positivity. The complete constraint enforcement mechanism maintains differentiability based on gradient optimization while strictly adhering to the constraint conditions determined by the physical laws of the Riemann problem.

[0127] In one embodiment, setting the physical information loss function for the multi - medium exact Riemann solver: As a pure unsupervised learning framework, the loss function of the multi - medium exact Riemann solver PINN - MERS completely comes from the physical constraints derived from the governing equations of the Riemann problem.

[0128] Specifically, the wave system structure of the solution is determined by the initial state, generating four left / right wave type combinations: shock - shock (S - S), shock - rarefaction (S - R), rarefaction - shock (R - S), rarefaction - rarefaction (R - R). Each combination requires specific physical constraints in the loss function, and the wave type is determined by entropy condition analysis before each training iteration.

[0129] The set physical information loss function is a composite loss function, which combines left / right wave contributions depending on the operating conditions:

[0130] ;

[0131] Among them, the S-S combination represents the shock-shock combination, the S-R combination represents the shock-rarefaction wave combination, the R-S combination represents the rarefaction wave-shock combination, and the R-R combination represents the rarefaction wave-rarefaction wave combination. Represents the shock loss of the left wave. Represents the rarefaction wave loss of the left wave. Represents the shock loss of the right wave. Represents the rarefaction wave loss of the right wave. Is the binary weighting coefficient used to activate the corresponding wave pair combination.

[0132] Among them, for the shock wave that satisfies the Rankine-Hugoniot condition, its loss term is defined as:

[0133] ;

[0134] Among them, N Is the number of initial condition sets. Represents the th sample's shock wave velocity.

[0135] For the rarefaction wave controlled by the integral form, its loss term is constructed as:

[0136] ;

[0137] The path integral is numerically approximated using the fourth-order Runge-Kutta method, and the integration step size is , where it is determined according to experience Can better balance the calculation accuracy and efficiency.

[0138] The training process is to minimize this physical information loss function in the case of unlabeled data, adopt the L-BFGS optimization strategy, and update the network parameters by calculating the gradient through backpropagation.

[0139] Regarding the above step S18, its numerical discretization format is 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.

[0140] The specific implementation is as follows:

[0141] ;

[0142] Among them, Represents the spatial discretization operator acting on the conserved variable U .

[0143] The fourth-order WENO scheme reconstructs the cell interface flux through a convex combination of low-order polynomials. The combination weights are determined based on the smoothness of the solutions on each template, and smaller weights are assigned to discontinuous templates. In one dimension, the spatial discretization operator of the fourth-order WENO scheme can be expressed as:

[0144] ;

[0145] where and are the numerical fluxes at the cell interface, calculated through WENO reconstruction.

[0146] To ensure numerical stability, the time step is controlled by the CFL condition:

[0147] ;

[0148] where is the spatial step size, is the velocity vector, is the speed of sound, is the Courant number (usually taking a value less than 1), and the maximum value is calculated at all grid points to ensure global satisfaction of the condition.

[0149] In the above prediction scheme, by embedding the governing equations and constraint conditions of the multi-medium Riemann solver into the loss function and structure of the neural network, deep learning modeling under physical constraints is completed, and an accurate multi-medium Riemann solver based on PINNs (PINN-MERS) is realized. Input the original variable values of the initial state , and output the variable values of the star region state . The essence of the multi-medium accurate Riemann solver is to learn the mapping relationship between the input variables and output variables through the training of the physics-informed neural network. By introducing hard constraints in the neural network, the output results strictly comply with the physical constraints specified by the Riemann problem, reducing the dimensionality of the solution space and accelerating convergence. In the Eulerian framework, by combining the improved virtual fluid method (MGFM) with PINN-MERS, accurate numerical simulations of multi-medium interactions in complex engineering cases are realized.

[0150] The above multi-medium accurate Riemann solver can stably and accurately solve the multi-medium Riemann problem and predict the state after multi-medium interaction. Compared with traditional approximate Riemann solvers, the multi-medium accurate Riemann solver proposed in this specification has higher accuracy, is more stable, does not exhibit non-convergence, and can always give relatively accurate prediction results. It is applicable to media with complex equations of state.

[0151] In some embodiments, in order to verify the effectiveness of the proposed method above, one-dimensional shock tube problems were used for experiments. The experiments involved a variety of media, including gases and rapidly expanding substances, and the material model parameters corresponding to different media are as follows: Gas 1 takes , Gas 2 takes , and the rapidly expanding substance takes , , , , , .

[0152] Four cases were set up in the experiment. The corresponding media on the left and right sides and the values of the initial primitive variables are shown in Table 1. The units of density, velocity, and pressure are . Among them, TC1 and TC2 have the same media on the left and right. By setting different initial conditions, the corresponding wave systems are R-R and S-S respectively. TC3 and TC4 have different media on the left and right sides. Table 2 shows the comparison of the calculation results and errors 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. And as the equation of state becomes more complex, the errors also become larger, but the accuracy is always higher than that of the traditional approximate Riemann solver HLLC.

[0153] Table 1

[0154]

[0155] Table 2

[0156]

[0157] It should be understood that although the various steps in the above process Figure 1 are shown in sequence according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise clearly stated in this article, the execution of these steps has no strict order limit, and these steps can be executed in other orders. Moreover, at least a part of the steps of the above process Figure 1 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 sequential either, but can be executed alternately or in turn with at least a part of other steps or sub-steps or stages of other steps.

[0158] In one embodiment, as Figure 5As shown in the figure, a state prediction system 100 for multi-medium fluid interaction is provided, including 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 propulsion 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-medium fluid by 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 by using an extension equation. The Riemann construction module 15 is used to construct a local multi-medium Riemann problem in the interface normal direction. The solution prediction module 17 is used to solve the local multi-medium Riemann problem by using the constructed multi-medium exact Riemann solver, predict the output vector of the star region state solution of the local multi-medium Riemann problem, and the star region state is used as the state after the interaction at the multi-medium interface; the input vector of the multi-medium exact Riemann solver includes all initial variables of the local multi-medium Riemann problem, and the output vector of the multi-medium exact Riemann solver includes the left-traveling wave velocity, the right-traveling wave velocity, the star region velocity, the star region pressure, and the densities on both sides of the contact discontinuity. The multi-medium exact 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 second extension module 19 is used to perform a second normal extension on the output vector of the multi-medium exact Riemann solver; the flow field propulsion module 21 is used to perform space-time discretization and solution of the control equation by using a high-order method; among them, fourth-order WENO reconstruction is used for space calculation and third-order TVD Runge-Kutta format is used for time advancement. The interface update module 23 is used to advance the multi-medium interface according to the flow field result after space-time discretization and solution, and perform periodic re-initialization to maintain the signed distance property. The iterative output module 25 is used to jump to the interface calculation module, loop and iterate until the final simulation time, and output the numerical simulation result of the multi-medium fluid interaction.

[0159] For the above state prediction system 100 for multi-medium fluid interaction, by embedding the control equation and constraint conditions of multi-medium Riemann solution into the loss function and structure of the neural network, deep learning modeling under physical constraints is completed, and a multi-medium exact Riemann solver based on PINNs is realized, so as to learn the mapping relationship between input variables and output variables through physical information neural network training, and make the output result strictly comply with the physical constraints specified by the Riemann problem, reduce the dimensionality of the solution space and accelerate convergence. Finally, in the Euler framework, the numerical simulation of multi-medium interaction in complex engineering cases is realized, the multi-medium Riemann problem can be solved stably and accurately, the state after multi-medium interaction can be predicted, the prediction accuracy is higher, and it is applicable to media with complex equations of state.

[0160] In one embodiment, the hard constraint conditions of the multi-medium exact Riemann solver include:

[0161] ;

[0162] Among them, represents the star region velocity, represents the star region pressure, represents the left - traveling wave velocity, represents the right - traveling wave velocity, and represent the densities on both sides of the contact discontinuity. Softplus(·) is a smooth and strictly positive activation function.

[0163] In one embodiment, the set physical information loss function of the multi - medium exact Riemann solver is:

[0164] ;

[0165] Among them, the S - S combination represents the shock - shock combination, the S - R combination represents the shock - rarefaction wave combination, the R - S combination represents the rarefaction wave - shock combination, and the R - R combination represents the rarefaction wave - rarefaction wave combination. represents the shock loss of the left wave, represents the rarefaction wave loss of the left wave, represents the shock loss of the right wave, represents the rarefaction wave loss of the right wave, is the binary weighting coefficient.

[0166] For the specific limitations of the above - mentioned state prediction system 100 for multi - medium fluid interaction, reference can be made to the corresponding limitations of the state prediction method for multi - medium fluid interaction in the above text, which will not be elaborated here.

[0167] In one embodiment, a computer device is further 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 position of the material interface of a multi-media fluid and calculating the interface normal vector; performing a first normal extension according to the interface normal vector using an extension equation; constructing a local multi-media Riemann problem in the interface normal direction; using the constructed multi-media exact 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, and the star region state being the state after interaction at the multi-media interface; the input vector of the multi-media exact Riemann solver includes all initial variables of the local multi-media Riemann problem, and the output vector of the multi-media exact Riemann solver includes the left-traveling wave velocity, the right-traveling wave velocity, the star region velocity, the star region pressure, and the densities on both sides of the contact discontinuity. The multi-media exact Riemann solver is a fully connected neural network architecture and uses the L-BFGS optimization strategy to minimize a set physical information loss function for optimization and solution; performing a second normal extension on the output vector of the multi-media exact Riemann solver; after the second normal extension, using a high-order method to perform space-time discretization and solution of the control equations; wherein, fourth-order WENO reconstruction is used for spatial calculation and third-order TVD Runge-Kutta format is used for time advancement; advancing the multi-media interface according to the calculated flow field results and performing periodic re-initialization to maintain the signed distance property; returning 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 calculating the interface normal vector, and iteratively executing the loop until the final simulation time, and outputting the numerical simulation results of the interaction of the multi-media fluid.

[0168] In one embodiment, when the processor executes the computer program, the processing steps of the state prediction method for the interaction of multi-media fluids in the above-mentioned other embodiments can also be implemented.

[0169] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. 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 methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided by the present invention can include non-volatile and / or volatile memories. 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. By way of 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 (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), memory bus dynamic random access memory (Rambus DRAM, abbreviated as RDRAM), and interface dynamic random access memory (DRDRAM), etc.

[0170] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, 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, it should be considered as the scope described in this specification.

[0171] The above embodiments only represent several implementation manners of the present invention, and their descriptions are relatively specific and detailed. However, it should not be understood as a limitation to the protection scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, which all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.

Claims

1. A method for predicting the state of multi-medium fluid interaction, characterized in that, Including the steps: Using a level set function to track and capture the position of the material interface of the multi - medium fluid and calculating the interface normal vector; Performing the first normal extension according to the interface normal vector using an extension equation; Constructing a local multi - medium Riemann problem in the interface normal direction; Using the constructed multi - medium exact 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, and the star - region state being the state after interaction at the multi - medium interface; The input vector of the multi - medium exact Riemann solver includes all initial variables of the local multi - medium Riemann problem, the output vector of the multi - medium exact Riemann solver includes the left - traveling wave velocity, the right - traveling wave velocity, the star - region velocity, the star - region pressure, and the densities on both sides of the contact discontinuity. The multi - medium exact Riemann solver is a fully - connected neural network architecture and is optimized using the L - BFGS optimization strategy to minimize a set physical information loss function; Performing a second normal extension on the output vector of the multi - medium exact Riemann solver; After the second normal extension, using a high - order method to perform space - time discretization and solve the governing equations; among them, using fourth - order WENO reconstruction for spatial calculation and third - order TVD Runge - Kutta format for time marching; Advancing the multi - medium interface according to the flow - field results calculated by the space - time discretization solution, and performing periodic re - initialization to maintain the signed - distance property; Returning to the step of using a level set function to track and capture the position of the material interface of the multi - medium fluid and calculating the interface normal vector, and iteratively executing the loop until the final simulation time, and outputting the numerical simulation results of the interaction of the multi - medium fluid.

2. The state prediction method for multi-media fluid interaction according to claim 1, wherein The hard - constraint conditions of the multi - medium exact Riemann solver include: Among them, represents the stellar velocity, represents the stellar pressure, represents the left - traveling wave velocity, represents the right - traveling wave velocity, and represent the densities on both sides of the contact discontinuity. Softplus(·) is a smooth and strictly positive activation function.

3. The state prediction method for multi-media 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, the S-S combination represents the shock-shock combination, the S-R combination represents the shock-rarefaction wave combination, the R-S combination represents the rarefaction wave-shock combination, and the R-R combination represents the rarefaction wave-rarefaction wave combination. represents the shock loss of the left wave. represents the rarefaction wave loss of the left wave. represents the shock loss of the right wave. represents the rarefaction wave loss of the right wave. is the binary weighting coefficient.

4. A state prediction system for the interaction of multi-media fluids, characterized in that, Including: An interface calculation module for using a level set function to track and capture the position of the material interface of the multi - medium fluid and calculating the interface normal vector; A first - extension module for performing the first normal extension according to the interface normal vector using an extension equation; A Riemann construction module for constructing a local multi - medium Riemann problem in the interface normal direction; A solution prediction module for using the constructed multi - medium exact 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, and the star - region state being the state after interaction at the multi - medium interface; The input vector of the multi - medium exact Riemann solver includes all initial variables of the local multi - medium Riemann problem, the output vector of the multi - medium exact Riemann solver includes the left - traveling wave velocity, the right - traveling wave velocity, the star - region velocity, the star - region pressure, and the densities on both sides of the contact discontinuity. The multi - medium exact Riemann solver is a fully - connected neural network architecture and is optimized using the L - BFGS optimization strategy to minimize a set physical information loss function; A second - extension module for performing a second normal extension on the output vector of the multi - medium exact Riemann solver; A flow - field advancement module for using a high - order method to perform space - time discretization and solve the governing equations; among them, using fourth - order WENO reconstruction for spatial calculation and third - order TVD Runge - Kutta format for time marching; The interface update module is used to advance the multi - medium interface according to the flow field results calculated by the spatio - temporal discrete solution, and perform periodic re - initialization to maintain the signed distance property; The iterative output module is used to jump to the interface calculation module, and perform loop iteration until the final simulation time, and output the numerical simulation results of the multi - medium fluid interaction.

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

6. The state prediction system for multi-media 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, the S-S combination represents the shock-shock combination, the S-R combination represents the shock-rarefaction wave combination, the R-S combination represents the rarefaction wave-shock combination, and the R-R combination represents the rarefaction wave-rarefaction wave combination. represents the shock loss of the left wave. represents the rarefaction wave loss of the left wave. represents the shock loss of the right wave. represents the rarefaction wave 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, it implements the steps of the state prediction method for multi - medium fluid interaction according to any one of claims 1 to 3.

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