Numerical simulation method and device for hypersonic flow field and electronic equipment

Abstract

The application provides a numerical simulation method and device for a hypersonic flow field and an electronic device, including establishing a three-dimensional space discrete model based on a parabolic Navier-Stokes equation, arranging flow variables at the center of a control volume surface formed by adjacent sections along a main flow direction; introducing a pressure gradient splitting mechanism in the calculation of a flow direction flux, forming a flow direction inviscid Jacobian matrix by directional processing of the pressure gradient on the current section in combination with the relationship between the conservative variables and the grid geometric derivative; constructing a corresponding transverse inviscid Jacobian matrix and obtaining its spectral radius information, calculating a transverse viscous flux based on a central difference format, and constructing an implicit correction equation, splitting the lower triangular, upper triangular and diagonal parts of the coefficient matrix, solving a block diagonal system through forward scanning and backward scanning, obtaining variable increments of the next section and updating the flow parameters, and realizing numerical simulation of the hypersonic flow field.

Description

Technical Field

[0001] This application relates to the field of computational fluid dynamics, and in particular to a numerical simulation method, apparatus, and electronic equipment for hypersonic flow fields. Background Technology

[0002] In numerical simulations of hypersonic flow fields, the parabolic Navier-Stokes (PNS) equations are often solved using spatial propagation methods to improve computational efficiency. Existing methods are mostly based on the ADI scheme for implicit solutions, involving multiple inversions of the block tridiagonal matrix, resulting in significant computational overhead. Furthermore, for transverse inviscid fluxes, using a central scheme requires introducing artificial dissipation, parameter tuning relies on experience, and affects the physical consistency of the results; using FDS-like schemes such as the Roe scheme presents problems such as unmet entropy conditions, expanding shock waves, and computational instability. Moreover, traditional schemes struggle to balance numerical stability with low dissipation, limiting the accurate capture of shock waves and boundary layer disturbances in complex flow fields, thus impacting overall simulation accuracy and convergence efficiency. Summary of the Invention

[0003] The purpose of this application is to provide a numerical simulation method, apparatus, and electronic device for hypersonic flow fields, so as to alleviate the above-mentioned technical problems existing in the prior art.

[0004] In a first aspect, the present invention provides a numerical simulation method for hypersonic flow fields, comprising: A three-dimensional spatial discrete model is established based on the parabolic Navier-Stokes equations. The flow variables are arranged at the center of the control volume formed by adjacent cross sections along the mainstream direction, and the time derivative term and the viscous stress and heat conduction components in the mainstream direction are removed. In the calculation of flow flux, a pressure gradient splitting mechanism is introduced. By directional processing of the pressure gradient on the current section, and combining the relationship between the conserved variables and the geometric derivative of the grid, the flow inviscid flux is linearized to form the flow inviscid Jacobian matrix. A hybrid upwind scheme is used to calculate the transverse inviscid flux, and its propagation direction is separated by the vector flux splitting method. The corresponding transverse inviscid Jacobian matrix is ​​constructed and its spectral radius information is obtained. At the same time, the transverse viscous flux is calculated based on the central difference scheme. An implicit correction equation is constructed by combining the linearization results of the flow direction and the transverse flux. The coefficient matrix is ​​split into lower triangular, upper triangular and diagonal parts by LU-SGS factorization strategy. The block diagonal system is solved by forward and backward scanning to obtain the variable increment of the next section and update the flow parameters, so as to realize the numerical simulation of the hypersonic flow field.

[0005] In an optional implementation, a pressure gradient splitting mechanism is introduced into the flow flux calculation. By directional processing of the pressure gradient on the current cross section and combining the relationship between conserved variables and the mesh geometric derivative, the flow inviscid flux is linearized to form a flow inviscid Jacobian matrix, including: By removing the upstream propagation information portion of the flow-direction pressure gradient, the local rate of change of the flow-direction inviscid flux with respect to the conserved variables is calculated using the conserved variables of the current section and the mesh geometric derivative. This rate of change is then fixed to the current spatial layer using a finite volume discretization scheme, and the corresponding coefficient matrix block is constructed to form the flow-direction inviscid Jacobian matrix.

[0006] In an optional implementation, a hybrid upwind scheme is used to calculate the transverse inviscid flux, and its propagation direction is separated by a vector flux splitting method. The corresponding transverse inviscid Jacobian matrix is ​​then constructed, and its spectral radius information is obtained, including: Calculate the transverse convection flux of the continuity, momentum, and energy equations, and split the convection flux into positive and negative parts according to the convection Mach number; The weighted flux is decomposed into positive and negative propagation components according to the propagation direction. The positive and negative parts of the transversely inviscid Jacobian matrix are constructed based on the positive and negative propagation components, respectively. The total spectral radius information is determined by using the absolute value of the largest eigenvalue of the transversely inviscid flux Jacobian matrix. The construction of the transversely inviscid Jacobian matrix and its spectral radius information are completed.

[0007] In an optional implementation, the transverse viscous flux is calculated based on the central difference scheme, including: Based on the velocity gradient and temperature gradient on the current mainstream cross section, the viscous stress term and heat conduction term are calculated using the central difference scheme respectively; The calculated viscous stress and heat conduction terms are combined into a transverse viscous flux, which is then used as an explicit contribution to the flux aggregation of the current space layer to calculate the transverse viscous flux.

[0008] In an optional implementation, an implicit correction equation is constructed by combining the linearization results of the flow direction and the lateral flux, including: The linearized residual terms after forming the flow-inviscid Jacobian matrix, constructing the transverse inviscid Jacobian matrix and obtaining its spectral radius information are integrated. The implicit contribution of viscous flux to the increment of the conserved variable is ignored, and only its calculated value at the current spatial layer is retained as the residual input. A system of linear equations with the increment of the conserved variable as the unknown is formed by discretizing the scheme using the finite volume method, and the implicit correction equation is constructed.

[0009] In an optional implementation, the coefficient matrix is ​​split into lower triangular, upper triangular, and diagonal parts using the LU-SGS factorization strategy, including: The spectral radii of the flow-inviscid Jacobian matrix, the transversely inviscid Jacobian matrix, and the viscous Jacobian matrix are added together to obtain a unified splitting scalar parameter. The total coefficient matrix is ​​directionally decomposed based on the splitting scalar parameter. The part representing upstream dependencies is assigned to the lower triangular terms, the part representing downstream dependencies is assigned to the upper triangular terms, and the locally dominant terms are retained in the diagonal terms, so as to perform matrix splitting under the LU-SGS factorization strategy.

[0010] In an optional implementation, the block diagonal system is solved by forward and backward scanning to obtain the variable increment of the next section and update the flow parameters, including: Using the flow state of the previous main cross section as the initial condition, the lower triangular system is solved by sequentially performing a forward scan process along the grid points to obtain the intermediate correction amount; The upper triangular system is solved by performing a backward scan process based on the intermediate correction amount, and the increment of the conserved variable on each control surface is obtained. The increments of the conserved variables are superimposed on the flow parameters of the current spatial layer to update the flow parameters on the next mainstream cross section.

[0011] Secondly, the present invention provides a numerical simulation apparatus for hypersonic flow fields, comprising: The spatial discrete modeling unit is used to establish a three-dimensional spatial discrete model based on the parabolic Navier-Stokes equations. The flow variables are arranged at the center of the control volume surface formed by adjacent cross sections along the mainstream direction, and the time derivative term and the viscous stress and heat conduction components in the mainstream direction are removed. The flow flux processing unit is used to introduce a pressure gradient splitting mechanism in the flow flux calculation. By directional processing of the pressure gradient on the current section, and combining the relationship between the conserved variables and the mesh geometric derivative, the flow inviscid flux is linearized to form the flow inviscid Jacobian matrix. The transverse flux processing unit is used to calculate the transverse inviscid flux using a hybrid upwind scheme, separate its propagation direction using the vector flux splitting method, construct the corresponding transverse inviscid Jacobian matrix and obtain its spectral radius information, and calculate the transverse viscous flux based on the central difference scheme. The implicit solution update unit is used to construct implicit correction equations by combining the linearization results of the flow direction and transverse flux. The coefficient matrix is ​​split into lower triangular, upper triangular and diagonal parts by using the LU-SGS factorization strategy. The block diagonal system is solved by forward and backward scanning to obtain the variable increment of the next section and update the flow parameters, so as to realize the numerical simulation of hypersonic flow field.

[0012] Thirdly, the present invention provides an electronic device including a processor and a memory, the memory storing computer-executable instructions that can be executed by the processor, the processor executing the computer-executable instructions to implement the numerical simulation method for hypersonic flow fields according to any of the foregoing embodiments.

[0013] Fourthly, the present invention provides a computer-readable storage medium storing computer-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the numerical simulation method for hypersonic flow fields according to any of the foregoing embodiments.

[0014] The numerical simulation method, apparatus, and electronic equipment for hypersonic flow fields provided in this application employ a LU-SGS implicit scheme for spatial propagation, requiring only the inversion of the block diagonal matrix, significantly reducing the computational overhead of solving the block tridiagonal matrix in the ADI scheme and improving convergence efficiency. A pressure gradient splitting mechanism is introduced to enhance the numerical stability of flow propagation and avoid non-physical oscillations. The transverse inviscid flux uses a hybrid upwind scheme such as AUSMPW, accurately capturing shock waves without artificial dissipation, overcoming the problems of parameter adjustment dependence in the central scheme and the tendency of the FDS scheme to fail to meet the entropy increase condition. By combining vector flux splitting and spectral radius estimation, a Jacobian matrix is ​​rationally constructed, balancing stability and low dissipation. Overall, this application significantly reduces computational resource consumption while ensuring high-precision simulation of shock wave-boundary layer interference, making it suitable for efficient and stable numerical simulation of complex hypersonic flow fields. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the specific embodiments of this application or the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0016] Figure 1 A flowchart illustrating a numerical simulation method for hypersonic flow fields provided in this application embodiment; Figure 2 A schematic diagram of a PNS equation mesh element in a general curvilinear coordinate system provided in an embodiment of this application; Figure 3 A structural diagram of a numerical simulation device for hypersonic flow fields provided in an embodiment of this application; Figure 4 This is a structural diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0018] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0019] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0020] This application provides a numerical simulation method for hypersonic flow fields. See [link to relevant documentation]. Figure 1 As shown, the method mainly includes the following steps: S110 establishes a three-dimensional spatial discrete model based on the parabolic Navier-Stokes equations, arranges the flow variables at the center of the control volume formed by adjacent cross sections along the mainstream direction, and removes the time derivative term and the viscous stress and heat conduction components in the mainstream direction.

[0021] The parabolic Navier-Stokes equations refer to the simplified form of the Navier-Stokes equations under high Reynolds number and hypersonic flow conditions, neglecting time-dependent unsteady-state terms and mainstream viscous diffusion terms. Its mathematical properties are parabolic, allowing for layer-by-layer solution along the flow direction. The aforementioned three-dimensional discrete model is constructed based on the finite volume method. In a general curvilinear coordinate system, the computational domain is divided into multiple control volume elements. Each control volume consists of the mainstream plane of the current layer j and the next layer j+1, along with their transverse grid points. Flow variables (such as density, momentum, and energy conservation variables) are stored at the center of the control volume surface, rather than at nodes, which improves flux calculation accuracy and numerical stability. By removing the time derivative term and the mainstream viscous and thermal conduction terms, the equations acquire unidirectional propagation characteristics, making them suitable for simulating hypersonic flow fields with strong coupling between the boundary layer and external inviscid flow.

[0022] In practical applications, the three-dimensional PNS equations in a general curvilinear coordinate system are: (1) In the formula, , and They represent , and Flux in direction, subscript and These represent inviscid flux and viscous flux, respectively. Compared to the Navier-Stokes equations, the PNS equations omit time-unsteady terms, and the superscript "*" on the viscous term indicates that the approximate mainstream direction is ignored. The viscosity and thermal diffusivity terms (in the direction of flow). To ensure the stability of spatial propagation along the flow direction, only a portion of the pressure gradient is retained in the flow direction inviscid flux, i.e., the flow direction pressure gradient is split using the Vigneron method.

[0023] The PNS equations are discretized using the finite volume method, with mesh elements such as... Figure 2 As shown. The grid cells are composed of and It consists of two main flow planes and their corresponding grid points. Flow variables are stored at the centers of the grid surfaces marked with ·. The discretized form of the PNS equations is:

[0024] In the formula, superscript and express Directional space layer ( (For the current layer). and The coordinates correspond to and direction.

[0025] S120 introduces a pressure gradient splitting mechanism in the calculation of flow flux. By directional processing of the pressure gradient on the current section, and combining the relationship between the conserved variables and the geometric derivative of the grid, the flow flux inviscidity is linearized to form the flow inviscid Jacobian matrix.

[0026] The aforementioned pressure gradient splitting mechanism refers to the use of the Vigneron method to partially retain the flow-direction pressure gradient, specifically by omitting the upstream propagation portion of the gradient, i.e., the "elliptic information portion." By selectively retaining the flow-direction pressure gradient, only the component that promotes forward information transmission is introduced, thus avoiding numerical instability caused by backflow feedback due to pressure disturbances.

[0027] The aforementioned orientation processing of the current cross-sectional pressure gradient refers to judging the pressure change trend based on the local flow field state and adjusting its contribution weight in the flux accordingly. Combining the relationship between conserved variables and grid geometric derivatives, the flow-directed inviscid flux depends not only on fluid state parameters (such as velocity, temperature, and pressure) but also on the spatial rate of change of grid coordinate transformation (such as direction cosines and their gradients).

[0028] In practical implementation, the flux can be locally linearly approximated under the known current cross-sectional flow field conditions to obtain its sensitivity to small changes in conserved variables. This sensitivity is expressed in matrix form, specifically through the flow-inviscid Jacobian matrix. This flow-inviscid Jacobian matrix is ​​used to characterize the local response characteristics of the flow flux to changes in state variables.

[0029] Specifically, the flow flux linearization approximation is performed. Flow to flux Represented as a conserved variable and coordinate transformation derivative The function is given by: Then the residual on the new spatial layer is:

[0030] Due to the conservation variables Because it is unknown, it cannot be calculated directly. You can use the current spatial layer and To perform linearization, i.e.:

[0031] In the formula, the increment of the conserved variable is The flow direction to the inviscid Jacobian matrix is:

[0032] identity

[0033] Substituting the linearization of the flow flux into the first term of equation (2):

[0034] S130 employs a hybrid upwind scheme to calculate the transverse inviscid flux, and separates its propagation direction using the vector flux splitting method to construct the corresponding transverse inviscid Jacobian matrix and obtain its spectral radius information. Simultaneously, it calculates the transverse viscous flux based on the central difference scheme.

[0035] The aforementioned hybrid upwind scheme refers to a numerical flux calculation method that combines high resolution and good robustness. Preferably, this embodiment uses the AUSMPW scheme. The AUSMPW scheme can automatically identify the propagation direction of wave systems in the flow, providing sufficient numerical dissipation in the shock wave region to prevent oscillations, while maintaining low dissipation characteristics in smooth flow field regions. This enables high-fidelity simulation of complex structures such as shock waves and expansion waves, without the need for manually adding artificial viscosity terms, thus reducing dependence on empirical parameters.

[0036] The aforementioned vector flux splitting method refers to decomposing the transverse inviscid flux vector into positive and negative parts based on its characteristic propagation direction. The Steger-Warming splitting method is preferred to facilitate subsequent processing of information transmission behavior in different directions. Based on this splitting result, the linearized coefficient matrix of the transverse inviscid flux with respect to the changes in conserved variables, i.e., the transverse inviscid Jacobian matrix, can be further extracted to describe the response characteristics of the transverse flux to state perturbations.

[0037] Simultaneously, the modulus of the largest eigenvalue is extracted, called the spectral radius, which is used to regulate the stability range of the implicit operator. For transverse viscous flux, a central difference scheme is used for discretization. This method has second-order accuracy, is suitable for accurate simulation of viscous-dominated regions within the boundary layer, and does not introduce additional non-physical dissipation, ensuring the physical consistency of the solution.

[0038] When performing the lateral flux linearization approximation... and The flux in the direction can be uniformly written in the following nonlinear format:

[0039] In the formula, It is a hidden factor. ; express and . The linearization approximation is as follows:

[0040] for We can also obtain an expression similar to (11).

[0041] S140, combining the linearization results of flow direction and transverse flux, constructs an implicit correction equation. The coefficient matrix is ​​split into lower triangular, upper triangular and diagonal parts using the LU-SGS factorization strategy. The block diagonal system is solved by forward and backward scanning to obtain the variable increment of the next section and update the flow parameters, thus realizing the numerical simulation of hypersonic flow field.

[0042] The aforementioned linearization result combining flow direction and lateral flux refers to using the local sensitivity of fluxes in each direction to changes in conserved variables obtained in previous steps to construct the residual changes of the entire PNS equation into a linear algebraic system with respect to the increment of unknown variables, i.e., an implicit correction equation. This equation reflects how changes in the flow state at the next spatial section are affected by changes in flux at the current section, and is the foundation for achieving implicit solutions.

[0043] The implicit correction equation is to substitute the linearized relationships (9) and (11) of the flow direction and lateral flux into equation (2) to obtain:

[0044] In the formula, the right-hand term is

[0045] The flow-inviscid Jacobian matrix in the right-hand term is in the form before pressure gradient splitting.

[0046] To reduce computational complexity, viscous flux is not implicitly processed. The Steger-Warming vector flux splitting scheme is used to split the transverse inviscid flux into positive and negative parts, and equation (12) can be simplified to:

[0047] In the formula, and They are respectively and Jacobian matrices for positive / negative inviscid flux in different directions.

[0048] The implicit factor in equation (14) is decomposed into the following three parts using the LU-SGS method:

[0049] In the formula, It is a lower triangular matrix. It is an upper triangular matrix. It is a diagonal matrix.

[0050] The core of the LU-SGS factorization strategy is to approximate the complex banded sparse matrix system in the original problem into three easily tractable parts: a lower triangular part (L) representing upstream influence, a diagonal part (D) representing local equilibrium, and an upper triangular part (U) representing downstream influence. In the specific solution process, a forward scan, starting from the flow inlet, sequentially propagates correction information forward, gradually eliminating the influence of the lower triangular part; then a backward scan, tracing back from the outlet, compensates for the effect of the upper triangular part. Finally, the variable correction amount for the next section is obtained, and the flow field state parameters are updated accordingly, completing one spatial advance and covering the entire computational domain layer by layer, achieving efficient, stable, and high-precision numerical simulation of hypersonic flow fields.

[0051] The split inviscid flux Jacobian matrix is ​​constructed by splitting according to the spectral radius, i.e.:

[0052] In the formula, and It is the sum of the spectral radii of the Jacobian matrices of inviscid and viscous fluxes.

[0053] , and They are respectively

[0054] The LU-SGS method uses a front-scan and a back-scan approach to solve the problem, i.e.:

[0055] The method provided in this application significantly reduces the computational overhead of traditional ADI-type methods when dealing with block tridiagonal systems by introducing the LU-SGS implicit scheme into the spatial propagation solution of the PNS equations. Efficient convergence can be achieved by solving only the block diagonal system. The pressure gradient splitting mechanism effectively ensures the stability of the spatial propagation algorithm. The transverse inviscid flux uses the AUSMPW hybrid upwind scheme, accurately capturing the shock structure without artificial dissipation, avoiding the problems of empirical parameter dependence in the central scheme and entropy insufficiency that may occur in the FDS scheme. The Jacobian matrix is ​​constructed by combining vector flux splitting and spectral radius estimation, balancing robustness and low dissipation. The overall algorithm significantly improves computational efficiency while ensuring high-precision simulation of shock-boundary layer interference, making it suitable for fast and stable numerical solutions of complex hypersonic flow fields.

[0056] For ease of understanding, the numerical simulation method for hypersonic flow fields provided in this application will be described in detail below.

[0057] In an optional implementation, the pressure gradient splitting mechanism is introduced into the flow flux calculation. By directional processing of the pressure gradient on the current section and combining the relationship between the conserved variables and the grid geometric derivative, the flow inviscid flux is linearized to form a flow inviscid Jacobian matrix. In specific implementation, the upstream propagation part of the flow pressure gradient can be removed, and the local rate of change of the flow inviscid flux with respect to the conserved variables can be calculated using the conserved variables of the current section and the grid geometric derivative. The rate of change is fixed to the current spatial layer using the finite volume method discretization scheme, and the corresponding coefficient matrix block is constructed to form the flow inviscid Jacobian matrix.

[0058] The aforementioned removal of the upstream propagation information portion of the flow-direction pressure gradient also means omitting the upstream propagation information portion (elliptic information portion) of the flow-direction pressure gradient. The local rate of change refers to the sensitivity of the flow-direction inviscid flux to small changes in conserved variables (such as density, velocity, energy, etc.), and is used to characterize the linearization slope of the flux function under the current flow field state. The calculation of this rate of change depends on the known fluid state parameters of the current cross-section and the spatial derivatives involved in the grid coordinate transformation (such as the Jacobian transform coefficients and their derivatives). By substituting the flux expression after the pressure gradient split into the linearization framework, the partial derivatives of the flux with respect to the state variables are estimated based solely on the information of the current layer, without involving unknown quantities in the next cross-section. Under the finite volume method framework, this partial derivative relationship is discretized into coefficient matrix blocks associated with the grid cells and used as the contribution part of the flow-direction term in the implicit correction equation. The coefficient blocks of multiple cells are combined to form a complete flow-direction inviscid Jacobian matrix, which is used for the construction of implicit operators in the subsequent LU-SGS scheme, supporting efficient and stable variable update iterations.

[0059] To ensure the stability of the flow-direction spatial propagation, only a portion of the pressure gradient is retained in the flow-direction inviscid flux, i.e., the Vigneron method is used to split the flow-direction pressure gradient.

[0060] The above approach introduces a directional decomposition mechanism for the pressure gradient and combines it with current laminar flow field information to linearize the flux, avoiding the back-disturbance feedback problem caused by the introduction of the full pressure gradient and effectively preventing computational divergence. Furthermore, the Jacobian matrix constructed based on local conserved variables and geometric derivatives is suitable for stable simulation of strong shock waves and boundary layer disturbances in complex hypersonic flow fields.

[0061] Furthermore, the above-mentioned method uses a hybrid upwind scheme to calculate the transverse inviscid flux and separates its propagation direction using a vector flux splitting method to construct the corresponding transverse inviscid Jacobian matrix and obtain its spectral radius information. In specific implementation, this may include the following steps 1-1 to 1-2: Step 1-1: Calculate the transverse convection flux of the continuity, momentum, and energy equations, and split the convection flux into positive and negative parts according to the convection Mach number.

[0062] In practical implementation, the weight distribution of convective velocities is dynamically adjusted by assessing the local Mach number, achieving adaptive responses to different flow regions (such as subsonic, supersonic, and near shock waves). For example, in the shock wave region, the weight of the dominant convective term is increased to provide sufficient numerical dissipation and prevent non-physical oscillations; while in smooth flow fields, the dissipation intensity is reduced to maintain high-precision resolution. This weighting mechanism eliminates the need for manual setting of dissipation parameters, achieving an automatic balance between numerical stability and computational accuracy.

[0063] Steps 1-2 decompose the weighted flux into positive and negative propagation components according to the propagation direction. Based on the positive and negative propagation components, construct the positive and negative parts of the transversely inviscid Jacobian matrix, respectively. Use the absolute value of the largest eigenvalue of the transversely inviscid flux Jacobian matrix to determine the total spectral radius information, thus completing the construction of the transversely inviscid Jacobian matrix and obtaining its spectral radius information.

[0064] Decomposition by propagation direction refers to using vector flux splitting techniques (such as the Steger-Warming method) to separate the weighted transverse inviscid flux into a positive component propagating along the positive characteristic direction and a negative component propagating along the negative characteristic direction, based on the characteristic structure of its hyperbolic equation.

[0065] Constructing the positive and negative parts of the Jacobian matrix involves locally linearizing the positive and negative flux components with respect to the conserved variables, respectively, to obtain the corresponding Jacobian submatrices, which are used for the implicit directional processing in the subsequent LU-SGS scheme. Simultaneously, the absolute value of the largest eigenvalue of the transverse inviscid flux Jacobian matrix (i.e., the spectral radius) is taken as a key parameter for measuring local wave velocity and stability constraints. Finally, the positive and negative parts are merged to form a complete transverse inviscid Jacobian matrix, and its spectral radius information is output for the construction of diagonal terms in the implicit correction equations and for CFL condition control.

[0066] This approach, by separating the transverse inviscid flux according to physical mechanisms and combining it with Mach number adaptive weighting, effectively suppresses the excessive dissipation problem in smooth regions of traditional schemes while ensuring shock wave capture capability, thereby improving simulation accuracy and significantly enhancing the robustness and computational efficiency of space propulsion processes. The overall scheme requires no manual parameter adjustment and is suitable for high-fidelity, automated numerical simulation of multi-scale structures in complex hypersonic flow fields.

[0067] Furthermore, the above-mentioned calculation of transverse viscous flux based on the central difference scheme may include the following steps 2-1 to 2-2 in a specific implementation: Step 2-1: Based on the velocity gradient and temperature gradient on the current mainstream cross section, calculate the viscous stress term and heat conduction term respectively using the central difference scheme.

[0068] Velocity gradient and temperature gradient refer to the rate of change of flow variables in the transverse (i.e., non-mainstream) space, and are the physical driving forces behind viscous shear stress and heat conduction effects. Viscous stress is caused by the spatial non-uniformity of velocity and follows Newtonian fluid constitutive relations; heat conduction is driven by temperature gradient and satisfies Fourier's law of thermal conductivity.

[0069] The central difference scheme calculates the gradient information at the current grid surface or node by symmetrically interpolating the velocity or temperature values ​​at adjacent grid points, which can effectively reduce discretization errors while ensuring numerical stability.

[0070] In practical implementation, this format is applied to the transverse grid distribution within the currently known spatial layer, and differential operations are performed across elements or nodes on the velocity components and temperature field to obtain the local viscous stress tensor components and heat flux density.

[0071] Step 2-2: Combine the calculated viscous stress term and heat conduction term into a transverse viscous flux, and use this flux as an explicit contribution term to participate in the flux aggregation of the current space layer to calculate the transverse viscous flux.

[0072] The transverse viscous flux refers to a conserved flux vector composed of transverse viscous stress and heat conduction, including both momentum dissipation and energy dissipation. The viscous stress and heat conduction terms calculated in the preceding steps are combined as conserved variables to form a complete viscous flux vector. Due to the spatial propulsion characteristics and computational efficiency considerations of the PNS equations, this viscous flux is not implicitly processed in this invention; instead, it is directly substituted as a known quantity into the residual calculation of the current space layer, i.e., added as an explicit contribution term to the total flux balance.

[0073] This approach avoids complex linearization and Jacobian matrix construction of the viscosity term, significantly reducing computational complexity while maintaining sufficient accuracy. It is particularly suitable for simulating hypersonic flows where the viscosity effect changes relatively gently within the boundary layer at high Reynolds numbers.

[0074] Furthermore, the above-mentioned implicit correction equation is constructed by combining the linearization results of the flow direction and the transverse flux. In specific implementation, the linearized residual terms after forming the flow direction inviscid Jacobian matrix, constructing the transverse inviscid Jacobian matrix and obtaining its spectral radius information can be integrated. The implicit change contribution of viscous flux to the increment of the conserved variable is ignored, and only its calculated value in the current spatial layer is retained as the residual input. The linear equation system with the increment of the conserved variable as the unknown is formed by the finite volume method discretization scheme, and the implicit correction equation is constructed.

[0075] In practice, the integration of linearized residual terms involves combining the previously linearized changes in directional and transverse inviscid fluxes according to their spatial discretization relationships to form a variation expression for the total residual. Specifically, the linearization result for directional flux has been constructed into a directional inviscid Jacobian matrix based on pressure gradient splitting and the relationship between conserved variables and geometric derivatives. For transverse flux, a corresponding transverse inviscid Jacobian matrix has been established using a hybrid upwind scheme and vector flux splitting method, and its spectral radius information has been extracted for implicit operator construction. These Jacobian matrices collectively constitute the coefficient part of the implicit correction equation, reflecting the sensitive response of fluxes in each direction to small changes in conserved variables.

[0076] The implicit contribution of viscous flux to the increment of the conserved variable is ignored, meaning that the transverse viscous flux is not linearized with respect to the variable increment, i.e., its corresponding viscous Jacobian matrix is ​​not constructed. This is because the viscous term itself has local diffusion characteristics, and its coefficient changes relatively smoothly, having a small impact on the overall system stability in high Reynolds number flows. Therefore, to reduce computational complexity, this invention adopts an explicit processing strategy: the viscous flux value already calculated at the current spatial layer is directly used in the residual calculation, without incorporating it into the implicit iterative system. This approach avoids the differentiation of the viscous term and the additional matrix storage and solution process, significantly saving computational resources.

[0077] The process of discretizing linear equations using the finite volume method with the increments of conserved variables as unknowns involves performing a Taylor expansion of the discrete residuals of the PNS equations at the control volume level with respect to their independent variables (i.e., the conserved variables of the next section), retaining only first-order terms. This transforms the original nonlinear problem into a linear algebraic system with respect to the increments of variables. The left-hand side of this system consists of implicit operators formed by the Jacobian matrices of the flow direction and the transverse inviscid flux, while the right-hand side includes the actual residual values ​​of the current layer and the explicit contribution of the viscous flux. The resulting linear equations are the implicit correction equations, and their solution objective is to obtain the conserved variable corrections that bring the residuals close to zero, which are then used to update the flow field state of the next spatial layer.

[0078] Furthermore, the above-mentioned LU-SGS factorization strategy for splitting the coefficient matrix into lower triangular, upper triangular, and diagonal parts can, in practice, include the following steps 3-1 and 3-2: Step 3-1: Add the spectral radii of the flow-inviscid Jacobian matrix, the transverse inviscid Jacobian matrix, and the spectral radii of the viscous Jacobian matrix to obtain a unified splitting scalar parameter.

[0079] The spectral radius refers to the largest absolute value among all eigenvalues ​​of a given Jacobian matrix. It characterizes the maximum propagation velocity of the disturbance in the local flow field and is a key physical quantity for measuring numerical stability and implicit operator scaling. In this invention, the flow-directed inviscid Jacobian matrix and the transverse inviscid Jacobian matrix characterize the propagation characteristics of inviscid wave systems (such as shock waves and expansion waves) in different directions, and their spectral radii are determined by the velocity of the convective waves in the corresponding directions. The spectral radius of the viscous Jacobian matrix, on the other hand, reflects the local intensity of the viscous diffusion process, which is usually small but not negligible within the boundary layer.

[0080] The summation of the spectral radii mentioned above is not a simple algebraic summation, but rather a comprehensive upper limit for the local propagation speed based on a conservative estimate of the maximum impact speed of various physical mechanisms. This sum serves as a unified splitting scalar parameter, used for scaling control when approximating the decomposition of the total coefficient matrix, ensuring that the implicit operator can cover all possible perturbation propagation paths and improving the robustness of the algorithm.

[0081] Step 3-2: Perform directional decomposition on the total coefficient matrix according to the split scalar parameter. The part representing upstream dependency is assigned to the lower triangular term, the part representing downstream dependency is assigned to the upper triangular term, and the local dominant term is retained in the diagonal term, so as to perform matrix splitting under the LU-SGS factorization strategy.

[0082] Directional decomposition refers to dividing a large, sparse coefficient matrix formed after discretization into three parts according to the direction of information transmission, based on the spatial propagation characteristics of the flow: lower triangular terms (L), diagonal terms (D), and upper triangular terms (U). The lower triangular terms contain the influence of upstream grid points on the current point, reflecting forward dependencies; the upper triangular terms contain the potential feedback from downstream grid points to the current point, which is usually weaker in the PNS framework but still needs to be modeled; the diagonal terms retain the dominant contribution of the current grid point itself.

[0083] Using the splitting scalar parameters obtained in step 3-1, the Jacobian matrices of inviscid and viscous fluxes are separated directionally by weighting the spectral radius, ensuring that the implicit processing of each term is consistent with its physical propagation direction. This decomposition method follows the basic idea of ​​the LU-SGS (Lower-Upper Symmetric Gauss-Seidel) scheme, which uses approximate factorization techniques to transform the original complex implicit system into a form that can be solved point-by-point forward scan (L+D) and backward scan (U), avoiding global matrix inversion and greatly reducing computational costs.

[0084] Furthermore, the above-mentioned method of solving the block diagonal system through forward and backward scanning to obtain the variable increment of the next section and update the flow parameters can, in specific implementation, include the following steps 4-1 to 4-3: Step 4-1: Using the flow state of the previous mainstream cross section as the initial condition, perform a forward scan process along the grid points to solve the lower triangular system and obtain the intermediate correction amount.

[0085] The flow state of the previous mainstream section refers to the known distribution of conserved variables, including density, momentum, and energy, on all control surfaces of the currently advancing space layer, serving as the initial input conditions for solving the space propulsion problem. Forward scanning is the first stage of the LU-SGS method, primarily involving a point-by-point forward recursive solution to the approximate system composed of lower triangular and diagonal matrices.

[0086] In practice, the scanning starts from the inlet and proceeds sequentially from front to back according to the spatial arrangement of grid points. At each step, the updated information from upstream is used to apply a correction effect to the current point, thereby gradually eliminating the low-frequency error components in the residuals and finally outputting the intermediate correction amount.

[0087] Step 4-2: Based on the intermediate correction, perform a backward scan process to solve the upper triangular system and obtain the increment of the conserved variable on each control surface.

[0088] The backward scan is the second stage of the LU-SGS method, used to compensate for downstream dependencies not included in the forward scan. The upper triangular system corresponds to the part of the coefficient matrix that reflects the influence of downstream grid points on the current point. Under the unidirectional dominant flow characteristics of the PNS equations, this influence is relatively weak but still needs to be modeled to ensure numerical stability.

[0089] The backward scan starts from the outlet end and performs back-substitution calculations in reverse spatial direction. The intermediate correction amount obtained in the previous stage is used as input. Combined with the feedback information of the downstream processed points, the variable change amount of the current point is further corrected, and the complete conserved variable increment after bidirectional correction is output, that is, the state change amount of the next spatial layer relative to the current layer.

[0090] Step 4-3: The increment of the conserved variable is superimposed on the flow parameters of the current spatial layer in order to update the flow parameters on the next mainstream cross section.

[0091] Superposition refers to directly adding the increments of conserved variables obtained in step 4-2 to the original variable values ​​of the current cross-section, completing the state transition from the current spatial layer to the next spatial layer. This operation is performed at the center of each control volume surface, ensuring that the updated flow parameters (such as pressure, temperature, velocity, etc.) accurately reflect the new equilibrium state of the flow field downstream. After the update is completed, the flow field of the new layer becomes the known condition for the next round of advancement, and the entire process continues to advance along the mainstream direction until it covers the entire computational domain.

[0092] By combining forward and backward scans, this implementation achieves efficient solution of the implicit correction equations. While only involving block diagonal matrix inverse operations, it takes into account the influence of upstream dependencies and downstream feedback, significantly improving convergence speed and numerical stability. Combined with a spatial propagation strategy, this method can operate stably under large step sizes, greatly reducing computation time. The variable update process is concise and clear, suitable for rapid simulation of hypersonic flow fields with complex geometries, and possesses comprehensive advantages of high computational efficiency, low memory consumption, and strong engineering applicability.

[0093] Based on the above method embodiments, this application also provides a numerical simulation device for hypersonic flow fields, see [link to relevant documentation]. Figure 3 As shown, the device mainly includes the following parts: The spatial discrete modeling unit 310 is used to establish a three-dimensional spatial discrete model based on the parabolic Navier-Stokes equations. The flow variables are arranged at the center of the control volume surface formed by adjacent cross sections along the mainstream direction, and the time derivative term and the viscous stress and heat conduction components in the mainstream direction are removed. The flow flux processing unit 320 is used to introduce a pressure gradient splitting mechanism in the flow flux calculation. By directional processing of the pressure gradient on the current section, and combining the relationship between the conserved variables and the mesh geometric derivative, the flow inviscid flux is linearized to form the flow inviscid Jacobian matrix. The transverse flux processing unit 330 is used to calculate the transverse inviscid flux using a hybrid upwind scheme, separate its propagation direction using the vector flux splitting method, construct the corresponding transverse inviscid Jacobian matrix and obtain its spectral radius information, and calculate the transverse viscous flux based on the central difference scheme. The implicit solution update unit 340 is used to construct implicit correction equations by combining the linearization results of the flow direction and the transverse flux. It adopts the LU-SGS factorization strategy to split the coefficient matrix into lower triangular, upper triangular and diagonal parts. It solves the block diagonal system through forward and backward scanning to obtain the variable increment of the next section and update the flow parameters, thereby realizing the numerical simulation of the hypersonic flow field.

[0094] In one feasible implementation, the above-mentioned flow throughput processing unit 320 is specifically used for: By removing the upstream propagation information portion of the flow-direction pressure gradient, the local rate of change of the flow-direction inviscid flux with respect to the conserved variables is calculated using the conserved variables of the current section and the grid geometric derivative. The local rate of change is then fixed to the current spatial layer using the finite volume method discretization scheme, and the corresponding coefficient matrix block is constructed to form the flow-direction inviscid Jacobian matrix.

[0095] In one feasible implementation, the lateral throughput processing unit 330 is specifically used for: Calculate the transverse convection flux of the continuity, momentum, and energy equations, and split the convection flux into positive and negative parts according to the convection Mach number; The weighted flux is decomposed into positive and negative propagation components according to the propagation direction. The positive and negative parts of the transversely inviscid Jacobian matrix are constructed based on the positive and negative propagation components, respectively. The total spectral radius information is determined by using the absolute value of the largest eigenvalue of the transversely inviscid flux Jacobian matrix. The construction of the transversely inviscid Jacobian matrix and its spectral radius information are completed.

[0096] In one feasible implementation, the lateral throughput processing unit 330 is specifically used for: Based on the velocity gradient and temperature gradient on the current mainstream cross section, the viscous stress term and heat conduction term are calculated using the central difference scheme respectively; The calculated viscous stress and heat conduction terms are combined into a transverse viscous flux, which is then used as an explicit contribution to the flux aggregation of the current space layer to calculate the transverse viscous flux.

[0097] In one feasible implementation, the implicit solution update unit 340 described above is specifically used for: The linearized residual terms after forming the flow-inviscid Jacobian matrix, constructing the transverse inviscid Jacobian matrix and obtaining its spectral radius information are integrated. The implicit contribution of viscous flux to the increment of the conserved variable is ignored, and only its calculated value at the current spatial layer is retained as the residual input. A system of linear equations with the increment of the conserved variable as the unknown is formed by discretizing the scheme using the finite volume method, and the implicit correction equation is constructed.

[0098] In one feasible implementation, the implicit solution update unit 340 described above is specifically used for: The spectral radii of the flow-inviscid Jacobian matrix, the transversely inviscid Jacobian matrix, and the viscous Jacobian matrix are added together to obtain a unified splitting scalar parameter. The total coefficient matrix is ​​directionally decomposed based on the splitting scalar parameter. The part representing upstream dependencies is assigned to the lower triangular terms, the part representing downstream dependencies is assigned to the upper triangular terms, and the locally dominant terms are retained in the diagonal terms, so as to perform matrix splitting under the LU-SGS factorization strategy.

[0099] In one feasible implementation, the implicit solution update unit 340 described above is specifically used for: Using the flow state of the previous main cross section as the initial condition, the lower triangular system is solved by sequentially performing a forward scan process along the grid points to obtain the intermediate correction amount; The upper triangular system is solved by performing a backward scan process based on the intermediate correction amount, and the increment of the conserved variable on each control surface is obtained. The increments of the conserved variables are superimposed on the flow parameters of the current spatial layer to update the flow parameters on the next mainstream cross section.

[0100] The numerical simulation device for hypersonic flow fields provided in this application has the same implementation principle and technical effects as the aforementioned method embodiments. For the sake of brevity, any parts not mentioned in the embodiments of the numerical simulation device for hypersonic flow fields can be referred to the corresponding content in the aforementioned numerical simulation method embodiments for hypersonic flow fields.

[0101] This application also provides an electronic device, such as... Figure 4 The diagram shows the structure of the electronic device 100, which includes a processor 41 and a memory 40. The memory 40 stores computer-executable instructions that can be executed by the processor 41. The processor 41 executes the computer-executable instructions to implement any of the above-mentioned numerical simulation methods for hypersonic flow fields.

[0102] exist Figure 4 In the illustrated embodiment, the electronic device further includes a bus 42 and a communication interface 43, wherein the processor 41, the communication interface 43, and the memory 40 are connected via the bus 42.

[0103] The memory 40 may include high-speed random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device. Communication between this system network element and at least one other network element is achieved through at least one communication interface 43 (which can be wired or wireless), such as the Internet, wide area network, local area network, metropolitan area network, etc. The bus 42 may be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component Interconnect) bus, or an EISA (Extended Industry Standard Architecture) bus, etc. The bus 42 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 4 The symbol is represented by a single double-headed arrow, but this does not mean that there is only one bus or one type of bus.

[0104] Processor 41 may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the hardware of processor 41 or by instructions in software form. Processor 41 can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. The general-purpose processor can be a microprocessor or any conventional processor. The method disclosed in the embodiments of this application can be directly implemented by a hardware decoding processor, or by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. The storage medium is located in the memory. The processor 41 reads the information in the memory and, in conjunction with its hardware, completes the numerical simulation method for hypersonic flow fields described in the foregoing embodiments.

[0105] This application also provides a computer-readable storage medium storing computer-executable instructions. When these computer-executable instructions are called and executed by a processor, they cause the processor to implement the above-described numerical simulation method for hypersonic flow fields. For specific implementation details, please refer to the foregoing method embodiments, which will not be repeated here.

[0106] The computer program product for the numerical simulation method, apparatus and electronic device for hypersonic flow fields provided in the embodiments of this application includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the methods described in the preceding method embodiments. For specific implementation, please refer to the method embodiments, which will not be repeated here.

[0107] Unless otherwise specifically stated, the relative steps, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application.

[0108] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A numerical simulation method for hypersonic flow fields, characterized in that, include: A three-dimensional spatial discrete model is established based on the parabolic Navier-Stokes equations. The flow variables are arranged at the center of the control volume formed by adjacent cross sections along the mainstream direction, and the time derivative term and the viscous stress and heat conduction components in the mainstream direction are removed. In the calculation of flow flux, a pressure gradient splitting mechanism is introduced. By directional processing of the pressure gradient on the current section, and combining the relationship between the conserved variables and the geometric derivative of the grid, the flow inviscid flux is linearized to form the flow inviscid Jacobian matrix. A hybrid upwind scheme is used to calculate the transverse inviscid flux, and its propagation direction is separated by the vector flux splitting method. The corresponding transverse inviscid Jacobian matrix is ​​constructed and its spectral radius information is obtained. At the same time, the transverse viscous flux is calculated based on the central difference scheme. An implicit correction equation is constructed by combining the linearization results of the flow direction and the transverse flux. The coefficient matrix is ​​split into lower triangular, upper triangular and diagonal parts by LU-SGS factorization strategy. The block diagonal system is solved by forward and backward scanning to obtain the variable increment of the next section and update the flow parameters, so as to realize the numerical simulation of the hypersonic flow field.

2. The numerical simulation method for hypersonic flow fields according to claim 1, characterized in that, A pressure gradient splitting mechanism is introduced into the calculation of flow flux. By directionalizing the pressure gradient at the current cross section and combining the relationship between conserved variables and the mesh geometric derivative, the flow flux inviscidity is linearized, forming the flow flux inviscid Jacobian matrix, which includes: By removing the upstream propagation information portion of the flow-direction pressure gradient, the local rate of change of the flow-direction inviscid flux with respect to the conserved variables is calculated using the conserved variables of the current section and the grid geometric derivative. The local rate of change is then fixed to the current spatial layer using the finite volume method discretization scheme, and the corresponding coefficient matrix block is constructed to form the flow-direction inviscid Jacobian matrix.

3. The numerical simulation method for hypersonic flow fields according to claim 1, characterized in that, A hybrid upwind scheme is used to calculate the transverse inviscid flux, and its propagation direction is separated by a vector flux splitting method. The corresponding transverse inviscid Jacobian matrix is ​​constructed, and its spectral radius information is obtained, including: Calculate the transverse convection flux of the continuity, momentum, and energy equations, and split the convection flux into positive and negative parts according to the convection Mach number; The weighted flux is decomposed into positive and negative propagation components according to the propagation direction. The positive and negative parts of the transversely inviscid Jacobian matrix are constructed based on the positive and negative propagation components, respectively. The total spectral radius information is determined by using the absolute value of the largest eigenvalue of the transversely inviscid flux Jacobian matrix. The construction of the transversely inviscid Jacobian matrix and its spectral radius information are completed.

4. The numerical simulation method for hypersonic flow fields according to claim 1, characterized in that, The calculation of transverse viscous flux based on the central difference scheme includes: Based on the velocity gradient and temperature gradient on the current mainstream cross section, the viscous stress term and heat conduction term are calculated using the central difference scheme respectively; The calculated viscous stress and heat conduction terms are combined into a transverse viscous flux, which is then used as an explicit contribution to the flux aggregation of the current space layer to calculate the transverse viscous flux.

5. The numerical simulation method for hypersonic flow fields according to claim 1, characterized in that, An implicit correction equation is constructed by combining the linearization results of flow direction and lateral flux, including: The linearized residual terms after forming the flow-inviscid Jacobian matrix, constructing the transverse inviscid Jacobian matrix and obtaining its spectral radius information are integrated. The implicit contribution of viscous flux to the increment of the conserved variable is ignored, and only its calculated value at the current spatial layer is retained as the residual input. A system of linear equations with the increment of the conserved variable as the unknown is formed by discretizing the scheme using the finite volume method, and the implicit correction equation is constructed.

6. The numerical simulation method for hypersonic flow fields according to claim 1, characterized in that, The coefficient matrix is ​​split into lower triangular, upper triangular, and diagonal parts using the LU-SGS factorization strategy, including: The spectral radii of the flow-inviscid Jacobian matrix, the transversely inviscid Jacobian matrix, and the viscous Jacobian matrix are added together to obtain a unified splitting scalar parameter. The total coefficient matrix is ​​directionally decomposed according to the splitting scalar parameter. The part representing upstream dependencies is assigned to the lower triangular terms, the part representing downstream dependencies is assigned to the upper triangular terms, and the local dominant terms are retained in the diagonal terms, so as to perform matrix splitting under the LU-SGS factorization strategy.

7. The numerical simulation method for hypersonic flow fields according to claim 1, characterized in that, By solving the block diagonal system using forward and backward scans, the variable increments for the next cross section are obtained and the flow parameters are updated, including: Using the flow state of the previous main cross section as the initial condition, the lower triangular system is solved by sequentially performing a forward scan process along the grid points to obtain the intermediate correction amount; Based on the intermediate correction, a backward scan process is performed to solve the upper triangular system, and the increment of the conserved variable on each control surface is obtained. The increments of the conserved variables are superimposed on the flow parameters of the current spatial layer to update the flow parameters on the next mainstream cross section.

8. A numerical simulation device for hypersonic flow fields, characterized in that, include: space Discrete modeling unit is used to establish a three-dimensional spatial discrete model based on the parabolic Navier-Stokes equations. The flow variables are arranged at the center of the control volume surface formed by adjacent cross sections along the mainstream direction, and the time derivative term and the viscous stress and heat conduction components in the mainstream direction are removed. The flow flux processing unit is used to introduce a pressure gradient splitting mechanism in the flow flux calculation. By directional processing of the pressure gradient on the current section, and combining the relationship between the conserved variables and the mesh geometric derivative, the flow inviscid flux is linearized to form the flow inviscid Jacobian matrix. The transverse flux processing unit is used to calculate the transverse inviscid flux using a hybrid upwind scheme, separate its propagation direction using the vector flux splitting method, construct the corresponding transverse inviscid Jacobian matrix and obtain its spectral radius information, and calculate the transverse viscous flux based on the central difference scheme. The implicit solution update unit is used to construct implicit correction equations by combining the linearization results of the flow direction and transverse flux. The coefficient matrix is ​​split into lower triangular, upper triangular and diagonal parts by using the LU-SGS factorization strategy. The block diagonal system is solved by forward and backward scanning to obtain the variable increment of the next section and update the flow parameters, so as to realize the numerical simulation of hypersonic flow field.

9. An electronic device, characterized in that, It includes a processor and a memory, the memory storing computer-executable instructions that can be executed by the processor, the processor executing the computer-executable instructions to implement the numerical simulation method for hypersonic flow fields according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions that, when invoked and executed by a processor, cause the processor to implement the numerical simulation method for hypersonic flow fields as described in any one of claims 1 to 7.

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