A transonic flow numerical simulation method, system, device and medium

Abstract

The application relates to the technical field of computational fluid dynamics, and discloses a transonic flow numerical simulation method, system, device and medium, the method comprising the following steps: determining whether a flow field has a region with a Mach number greater than a preset value; if not, the entire flow field is a subsonic region and belongs to a non-shock region; if yes, a supersonic region exists; determining whether a shock wave exists between adjacent grid points or non-structured grid elements; if a shock wave exists, a shock wave region and a non-shock wave region are divided; for the shock wave region, a TVD format is used to discretize the spatial term of a control equation to obtain a TVD format discrete result of the shock wave region; for the non-shock wave region, a linear numerical format is used to discretize the spatial term of the control equation to obtain a linear format discrete result of the non-shock wave region; a flow field is updated by using a time advancing method; and if a residual error converges, a simulation result of the transonic flow numerical simulation is output. The application can realize efficient, high-precision and robust simulation of transonic flow.

Description

Technical Field

[0001] This application relates to the field of computational fluid dynamics, and in particular to a method, system, device and medium for numerical simulation of transonic flow. Background Technology

[0002] Transonic flow typically refers to flow at Mach numbers between 0.8 and 1.2. In computational fluid dynamics, the governing equations (Euler equations or Navier-Stokes equations) describing this flow are elliptic when the Mach number is less than 1 and hyperbolic when the Mach number is greater than 1. When the Mach number equals 1, singularities occur, making it easy for spurious shock waves or spurious shock wave oscillations to appear during numerical simulations. Shock wave oscillations are coupled with the flutter of transonic aircraft, which is extremely difficult to separate and seriously affects aircraft design and safety assessment.

[0003] Publicly available literature rarely focuses on numerical simulation methods specifically for transonic flows. Most studies directly employ computational fluid dynamics (CFD) software, whose core solvers are compressible flow solvers. The numerical methods within these solvers are primarily shock wave-capturing schemes, such as the Roe scheme, TVD scheme, and WENO scheme. While these schemes can capture transonic shock waves, they suffer from excessive dissipation in shock-free regions, leading to problems such as "smoothing out" of flow field details and inaccurate predictions of extreme aerodynamic loads. These issues severely hinder the refined design of aircraft.

[0004] Linear numerical schemes, compared to nonlinear numerical schemes that can capture shock waves, have advantages such as high accuracy, low computational cost, and fast convergence speed. However, in supersonic conditions, these schemes may produce spurious numerical fluctuations near the shock wave, reducing the reliability of the results and even directly causing calculation failure.

[0005] Existing simulation methods employ a partitioned computational strategy: a special numerical format is used near the shock wave, while a high-precision format is used elsewhere. However, due to the characteristics of transonic flow, such as the non-fixed location and weak intensity of the shock wave, traditional shock wave partitioning methods often miss or misjudge moving weak shock waves.

[0006] Since most regions in a real transonic flow field lack shock waves, these regions can benefit from the advantages of linear numerical schemes, such as high accuracy, low computational cost, and fast convergence. Near shock waves, the TVD scheme can robustly capture shock waves and avoid non-physical oscillations. By combining linear numerical methods with the TVD scheme, efficient, accurate, and robust simulations of transonic flows can be achieved, provided that shock waves in the transonic flow field can be accurately identified.

[0007] Since the flow control equations are elliptical in the subsonic region and hyperbolic in the supersonic region, and the hyperbolic control equations can provide shock wave solutions, it is difficult for a single numerical method to give ideal calculation results. Summary of the Invention

[0008] In view of this, this application provides a method, system, device and medium for numerical simulation of transonic flow, which divides the flow field into a region with shock waves and a region without shock waves. The TVD scheme is used in the region with shock waves and the linear numerical scheme is used in the region without shock waves. This method can achieve efficient, robust and high-precision solutions for transonic flow.

[0009] This application discloses a numerical simulation method for transonic flow, which includes:

[0010] Step 1: Generate a spatial mesh based on the geometry of the transonic vehicle, set the calculation conditions, and provide an initial flow field with a Mach number less than a preset Mach number; the spatial mesh includes multiple mesh points or multiple mesh cells; the calculation conditions include incoming flow velocity, direction, Mach number, temperature, Reynolds number, density, pressure, and governing equations; the governing equations include the Euler equations or the Navier-Stokes equations;

[0011] Step 2: Calculate the Mach number in the flow field;

[0012] Step 3: Based on the Mach number calculated in Step 2, determine whether there is a region in the flow field where the Mach number is greater than the preset value; if not, it means that the entire flow field is in the subsonic region and belongs to the shock wave-free region, and jump to Step 5; if it exists, there is a supersonic region, and proceed to Step 4.

[0013] Step 4: Determine whether there is a shock wave between adjacent grid points or unstructured grid cells. If there is a shock wave, divide the area into a shock wave region and a non-shock wave region.

[0014] Step 5: For the shock-prone regions identified in Step 4, the spatial terms of the control equations are discretized using the TVD scheme to obtain the TVD scheme discretization results for the shock-prone regions; for the shock-free regions identified in Step 3 or the shock-free regions identified in Step 4, the spatial terms of the control equations are discretized using a linear numerical scheme to obtain the linear scheme discretization results for the shock-free regions.

[0015] Step 6: Update the flow field using the time-progression method based on the TVD scheme discretization results in the shock wave region and the linear scheme discretization results in the shock wave-free region;

[0016] Step 7: Determine if the residuals have converged; if the residuals have not converged, jump to Step 2 and recalculate; if the residuals have converged, output the simulation results of the transonic flow numerical values; the simulation results include: shock wave region division information, and converged flow field core parameters; the flow field core parameters include Mach number, density, velocity, temperature, and pressure; the residuals are the sum of iterative differences of the physical quantities of the entire flow field obtained by solving the governing equations; the flow field physical quantities include density, velocity, temperature, and pressure.

[0017] Further, step 4 includes:

[0018] If the sound velocity in the flow field is equal in adjacent grid points or unstructured grid cells, then there is no shock wave between adjacent grid points or unstructured grid cells. Otherwise, calculate the Mach number between adjacent grid points or unstructured grid cells and match it with the Mach number in the gradient direction of the sound velocity. Based on the matching result, determine whether there is a shock wave between adjacent grid points or unstructured grid cells.

[0019] Further, the calculation of the Mach number between adjacent grid points or unstructured grid cells includes:

[0020] If the first The sound velocity in the flow field within the basic grid cell is less than that of the first cell. The sound velocity of the flow field within the basic grid cell is then determined with reference to the shock front. The basic grid cell is located on one side of the shock front, corresponding to the first cell before the shock wave appears. The basic grid unit is located on the other side of the shock front, corresponding to the appearance of the shock wave; when the spatial grid is a structured grid, the first... The basic unit of the grid is the first Grid point, the first The basic unit of the grid is the first Grid points; when the spatial grid is an unstructured grid, the first The basic unit of the grid is the first Grid cell, the first The basic unit of the grid is the first Grid cells;

[0021] Establish a local coordinate system, with its origin at a point on the shock front. The axis is parallel to the tangent at that point. The axis is perpendicular to the tangent at that point. shaft and shaft and The plane formed by the axes is perpendicular;

[0022] Fixing the local coordinate system on the shock front, along the normal to the shock front, the... The Mach number of the flow field within the basic grid cell is The components on the axis are , No. The Mach number of the flow field within the basic grid cell is The components on the axis are Based on the Rankine-Yugonniu shock wave relationship, the following equation is obtained:

[0023] (1)

[0024] in, It is the specific heat ratio of gases. The temperature of the flow field before the shock wave appears. The temperature of the flow field after the shock wave appears;

[0025] Temperature of the flow field before the shock wave appears Temperature of the flow field after the shock wave appears It is known that the value before the appearance of the shock wave can be obtained using formula (1). ;

[0026] The following formula is used to obtain the first... The basic unit of the grid corresponds to :

[0027] (2).

[0028] Further, calculating the Mach number in the gradient direction of the sound speed includes:

[0029] The Mach number in the gradient direction of the speed of sound is calculated using the following formula:

[0030] , (3)

[0031] in, Let be the component of the Mach number before the shock wave along the gradient direction of the sound speed. This represents the component of the Mach number following the shock wave along the gradient direction of the sound velocity. Let be the component of the velocity preceding the shock wave along the gradient of the speed of sound. This represents the component of the velocity following the shock wave along the gradient of the sound speed. For the first The sound velocity in the flow field within the basic grid cell. For the first The velocity of sound in the flow field within the basic grid cell.

[0032] Furthermore, the gradient of the sound velocity in the supersonic region is calculated using the following formula:

[0033] (4)

[0034] Where c is the speed of sound in the supersonic flow field. , , These correspond to the unit basis vectors on the x-axis, y-axis, and z-axis, respectively, and the directions of the unit basis vectors are consistent with the positive directions of the coordinate axes. Gradient symbol;

[0035] and The expressions are as follows:

[0036] (5)

[0037] (6)

[0038] in, , , These represent the flow field velocities in the direction of flow, normal direction, and spanwise direction before the shock wave appears. , , These represent the flow field velocities in the direction of flow, normal direction, and spanwise direction after the shock wave appears; The x-axis of the global coordinate system represents the flow direction; The y-axis of the global coordinate system represents the normal direction. The z-axis of the global coordinate system represents the span. When the global coordinate system is two-dimensional... and The values ​​of are all 0; the origin of the global coordinate system is a point on the leading edge of the transonic vehicle's geometry.

[0039] Furthermore, the method involves matching the Mach number along the gradient direction of the sound velocity, and based on the matching result, determining whether a shock wave exists between adjacent grid points or unstructured grid cells, including:

[0040] pass , , , The degree of matching between them determines the first Mesh basic unit and the first Are there shock waves between the basic grid cells?

[0041] If the first Mesh basic unit and the first If the Mach number between the basic grid elements satisfies formula (7), then the... Mesh basic unit and the first Shock waves exist between the basic grid cells; otherwise, the first Mesh basic unit and the first There are no shock waves between the basic grid cells;

[0042] (7)

[0043] in, It is a positive number.

[0044] Furthermore, the division of the shock wave region and the non-shock wave region includes:

[0045] The size of the shock region is related to the width of the grid template in the linear numerical format;

[0046] Let the width of the mesh template be k, and the width of the shock wave region be k. for:

[0047] (8)

[0048] Regarding the flow direction, the second-order upwind pattern is:

[0049] (9)

[0050] in, For the first The flux of the flow field within the basic grid cell is the TVD scheme discretization result of the region with shock waves. For the flow direction in the global coordinate system, For the sign of differentiation, for The derivative, The length of the basic unit of the adjacent grid. For the first Flux of the flow field within the basic grid cell For the first Flux of the flow field within the basic grid cell;

[0051] When the flow direction of the flow field is opposite to that from the first Mesh basic unit to the th When the basic grid cells are oriented in the same direction, if the shock wave appears at the th... Mesh basic unit and the first Between the basic grid units, then the first Flux of the flow field within the basic grid cell and the Flux of the flow field within the basic grid cell All will be affected by the shock wave;

[0052] When the flow direction of the flow field is opposite to that from the first Mesh basic unit to the th When the basic grid cells are oriented in opposite directions, if the shock wave appears at the th... Mesh basic unit and the first Between the basic grid units, then the first Flux of the flow field within the basic grid cell and the Flux of the flow field within the basic grid cell All will be affected by the shock wave;

[0053] Based on the width of the shock region, the space grid of the transonic vehicle is divided into shock-containing regions; the remaining part is the shockless region.

[0054] This application also discloses a transonic flow numerical simulation system for implementing the above-described method, comprising:

[0055] The initialization module is used to generate a spatial mesh based on the geometry of the transonic vehicle, set the calculation conditions, and provide an initial flow field with a Mach number less than a preset Mach number. The spatial mesh includes multiple mesh points or multiple mesh cells. The calculation conditions include the incoming flow velocity, direction, Mach number, temperature, Reynolds number, density, pressure, and governing equations. The governing equations include the Euler equations or the Navier-Stokes equations.

[0056] The first calculation module is used to calculate the Mach number in the flow field;

[0057] The judgment module is used to determine whether there is a region in the flow field with a Mach number greater than a preset value based on the calculated Mach number. If it does not exist, it means that the entire flow field is a subsonic region and belongs to a shock wave-free region, and jumps to the second calculation module. If it exists, there is a supersonic region, and enters the region division module.

[0058] The region division module is used to determine whether there is a shock wave between adjacent grid points or unstructured grid cells. If a shock wave exists, it divides the region into a shock wave region and a region without a shock wave.

[0059] The second calculation module is used to discretize the spatial terms of the control equations using the TVD scheme for the defined shock wave region, and obtain the TVD scheme discretization result of the shock wave region; for the region determined to be without shock wave or the defined without shock wave region, the spatial terms of the control equations are discretized using the linear numerical scheme, and the linear scheme discretization result of the without shock wave region is obtained.

[0060] The flow field update module is used to update the flow field using a time-progression method based on the TVD format discretization results in the shock wave region and the linear format discretization results in the shock wave-free region.

[0061] The simulation result output module is used to determine whether the residuals have converged. If the residuals have not converged, the system jumps to the first calculation module and performs the loop calculation again. If the residuals have converged, the simulation results of the transonic flow are output. The simulation results include: shock wave region division information and converged flow field core parameters. The flow field core parameters include Mach number, density, velocity, temperature, and pressure. The residuals are the sum of iterative differences of the physical quantities of the entire flow field obtained by solving the governing equations. The flow field physical quantities include density, velocity, temperature, and pressure.

[0062] This application also discloses an electronic device, including a memory and a processor, wherein the memory stores a computer program that, when executed by the processor, implements the method described above.

[0063] This application also discloses a computer-readable storage medium comprising a computer program or instructions that, when executed on a computer, cause the computer to perform the methods described above.

[0064] Due to the adoption of the above technical solution, this application has the following advantages:

[0065] 1. This application fully leverages the advantages of linear numerical schemes and TVD schemes by using a partitioned coupling method, while avoiding their disadvantages, thus achieving efficient and high-precision robust simulation of transonic flow fields.

[0066] 2. This application presents a novel shock wave identification method. When identifying shock waves, the coordinate system is established on the shock wave, thus enabling the identification of shock waves in transonic flow fields.

[0067] 3. This application relates to a method for sectional and hybrid simulation of transonic flow with and without shock waves. This method can not only ensure efficient and high-precision simulation in the region without shock waves, but also robustly capture shock waves and avoid non-physical shock wave oscillations. Attached Figure Description

[0068] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings.

[0069] Figure 1 This is a flowchart illustrating a transonic flow numerical simulation method according to an embodiment of this application.

[0070] Figure 2 This is a schematic diagram of the spatial grid of an embodiment of this application, using the Rae-2822 airfoil as an example.

[0071] Figure 3(a) is a schematic diagram of the structural mesh of an embodiment of this application.

[0072] Figure 3(b) is a schematic diagram of an unstructured mesh according to an embodiment of this application.

[0073] Figure 4 This is a schematic diagram of the shock wave affected area (i.e., the area with shock waves) according to an embodiment of this application.

[0074] Figure 5 This is a schematic diagram of pressure contour lines around the Rae-2822 airfoil according to an embodiment of this application.

[0075] Figure 6 This is a schematic diagram of the supersonic region of the Rae-2822 airfoil according to an embodiment of this application. Detailed Implementation

[0076] The present application will be further described in conjunction with the accompanying drawings and embodiments. The described embodiments are only some, not all, of the embodiments of the present application. All other embodiments obtained by those skilled in the art should fall within the protection scope of the embodiments of the present application.

[0077] This application proposes a hybrid numerical simulation scheme for transonic flow using a linear numerical scheme and a TVD (Transonic Wave Difference) scheme. This scheme employs a linear numerical scheme in the subsonic and supersonic regions without shock waves, while using a TVD scheme in the shock wave and its influence region. This combines the advantages of the linear numerical scheme (efficiency, high accuracy, and fast convergence) with the TVD scheme's robust shock wave capture capability, avoiding problems such as shock wave oscillations, spurious numerical fluctuations, and "smoothing out" of details that occur with traditional single-method approaches. To achieve this hybrid approach, this invention proposes a novel shock wave identification method and a shock wave influence region division method. These two methods can conveniently divide the numerical simulation region into "shock-free regions" and "shock-affected regions."

[0078] See Figure 1 This application provides an embodiment of a numerical simulation method for transonic flow, which includes:

[0079] Step 1: Generate a spatial mesh based on the geometry of the transonic vehicle, set the calculation conditions, and provide an initial flow field with a Mach number less than a preset Mach number to initiate numerical calculation; the spatial mesh includes multiple mesh points or multiple mesh cells; the calculation conditions include incoming flow velocity, direction, Mach number, temperature, Reynolds number, density, pressure, and governing equations; the governing equations include the Euler equations or the Navier-Stokes equations;

[0080] Step 2: Calculate the Mach number in the flow field;

[0081] Step 3: Based on the Mach number calculated in Step 2, determine whether there is a region in the flow field where the Mach number is greater than the preset value (the preset value can be 1.0); if not, it means that the entire flow field is in the subsonic region and belongs to the shock wave-free region, and jump to Step 5; if it exists, there is a supersonic region, and proceed to Step 4; the preset value can be a floating-point number.

[0082] Step 4: Determine whether there is a shock wave between adjacent grid points or unstructured grid cells. If there is a shock wave, divide the area into a shock wave region and a non-shock wave region.

[0083] Step 5: For the shock-prone regions identified in Step 4, the spatial terms of the control equations are discretized using the TVD scheme to obtain the TVD scheme discretization results for the shock-prone regions; for the shock-free regions identified in Step 3 or the shock-free regions identified in Step 4, the spatial terms of the control equations are discretized using a linear numerical scheme to obtain the linear scheme discretization results for the shock-free regions.

[0084] Step 6: Update the flow field using the time-progression method based on the TVD scheme discretization results in the shock wave region and the linear scheme discretization results in the shock wave-free region;

[0085] Step 7: Determine if the residuals have converged; if the residuals have not converged, jump to Step 2 and recalculate; if the residuals have converged, output the simulation results of the transonic flow numerical values; the simulation results include: shock wave region division information, and converged flow field core parameters; the flow field core parameters include Mach number, density, velocity, temperature, and pressure; the residuals are the sum of iterative differences of the physical quantities of the entire flow field obtained by solving the governing equations; the flow field physical quantities include density, velocity, temperature, and pressure.

[0086] Figure 2 A mesh diagram is provided using the Rea-2822 airfoil as an example. The initial flow field with a preset Mach number can be a uniform initial flow field with a Mach number of 0.5. This application embodiment has no special requirements for the TVD format; mature TVD formats from computational fluid dynamics textbooks or literature, such as the Roe format and NND format, can be directly selected. This application embodiment has no special requirements for the linear numerical format; mature linear numerical formats from computational fluid dynamics textbooks or literature, such as the linear upwind compact format and the third-order upwind offset format, can be directly selected. This application embodiment has no special requirements for the time-stepping method; mature time-stepping methods from computational fluid dynamics textbooks or literature, such as the Runge-Kutta method and the LU-SGS method, can be directly selected.

[0087] Optionally, step 4 includes:

[0088] If the sound velocity in the flow field is equal in adjacent grid points or unstructured grid cells, then there is no shock wave between adjacent grid points or unstructured grid cells. Otherwise, calculate the Mach number between adjacent grid points or unstructured grid cells and match it with the Mach number in the gradient direction of the sound velocity. Based on the matching result, determine whether there is a shock wave between adjacent grid points or unstructured grid cells.

[0089] Optionally, calculating the Mach number between adjacent grid points or unstructured grid cells includes:

[0090] If the first The sound velocity in the flow field within the basic grid cell (e.g., the grid point corresponding to number 1 in Figure 3(a), and the grid cell corresponding to number 1 in Figure 3(b)) is less than that of the first grid cell. The sound velocity of the flow field within the basic grid unit (e.g., the grid point corresponding to number 2 in Figure 3(a), and the grid unit corresponding to number 2 in Figure 3(b)) is then determined with the shock front as the reference frame. The basic grid cell is located on one side of the shock front, corresponding to the first cell before the shock wave appears. The basic grid unit is located on the other side of the shock front, corresponding to the appearance of the shock wave; when the spatial grid is a structured grid, the first... The basic unit of the grid is the first Grid point, the first The basic unit of the grid is the first Grid points; when the spatial grid is an unstructured grid, the first The basic unit of the grid is the first Grid cell, the first The basic unit of the grid is the first Grid cells;

[0091] Establish a local coordinate system, with its origin at a point on the shock front. The axis is parallel to the tangent at that point. The axis is perpendicular to the tangent at that point. shaft and shaft and The plane formed by the axes is perpendicular;

[0092] Fixing the local coordinate system on the shock front, along the normal to the shock front, the... The Mach number of the flow field within the basic grid cell is The components on the axis are , No. The Mach number of the flow field within the basic grid cell is The components on the axis are Based on the Rankine-Yugonniu shock wave relationship, the following equation is obtained:

[0093] (1)

[0094] in, It is the specific heat ratio of gases. The temperature of the flow field before the shock wave appears. The temperature of the flow field after the shock wave appears;

[0095] Temperature of the flow field before the shock wave appears Temperature of the flow field after the shock wave appears It is known that the value before the appearance of the shock wave can be obtained using formula (1). ;

[0096] The following formula is used to obtain the first... The basic unit of the grid corresponds to :

[0097] (2).

[0098] Optionally, calculating the Mach number in the gradient direction of the sound speed includes:

[0099] The Mach number in the gradient direction of the speed of sound is calculated using the following formula:

[0100] , (3)

[0101] in, Let be the component of the Mach number before the shock wave along the gradient direction of the sound speed. This represents the component of the Mach number following the shock wave along the gradient direction of the sound velocity. Let be the component of the velocity preceding the shock wave along the gradient of the speed of sound. This represents the component of the velocity following the shock wave along the gradient of the sound speed. For the first The sound velocity in the flow field within the basic grid cell. For the first The velocity of sound in the flow field within the basic grid cell.

[0102] Optionally, the gradient of sound velocity in the supersonic region can be calculated using the following formula:

[0103] (4)

[0104] Where c is the speed of sound in the supersonic flow field. , , These correspond to the unit basis vectors on the x-axis, y-axis, and z-axis, respectively, and the directions of the unit basis vectors are consistent with the positive directions of the coordinate axes. Gradient symbol;

[0105] and The expressions are as follows:

[0106] (5)

[0107] (6)

[0108] in, , , These represent the flow field velocities in the direction of flow, normal direction, and spanwise direction before the shock wave appears. , , These represent the flow field velocities in the direction of flow, normal direction, and spanwise direction after the shock wave appears; The x-axis of the global coordinate system represents the flow direction; The y-axis of the global coordinate system represents the normal direction. The z-axis of the global coordinate system represents the span. When the global coordinate system is two-dimensional... and The values ​​of are all 0; the origin of the global coordinate system is a point on the leading edge of the transonic vehicle's geometry.

[0109] Optionally, the process involves matching the Mach number along the gradient direction of the sound velocity, and determining, based on the matching result, whether a shock wave exists between adjacent grid points or unstructured grid cells, including:

[0110] pass , , , The degree of matching between them determines the first Mesh basic unit and the first Are there shock waves between the basic grid cells?

[0111] If the first Mesh basic unit and the first If the Mach number between the basic grid elements satisfies formula (7), then the... Mesh basic unit and the first Shock waves exist between the basic grid cells; otherwise, the first Mesh basic unit and the first There are no shock waves between the basic grid cells;

[0112] (7)

[0113] in, It is a positive number, which can be 0.0001, or it can be adjusted based on experience.

[0114] The purpose of defining the shock wave region is to prevent the mesh template of the linear numerical scheme from crossing the shock wave. Since the computation method used outside the shock wave influence region is a linear numerical scheme, which is mostly based on a mesh template of a certain width.

[0115] Optionally, the division of the shock wave region and the non-shock wave region includes:

[0116] The size of the shock region is related to the width of the grid template in the linear numerical format;

[0117] Let the width of the mesh template be k, and the width of the shock wave region be k. for:

[0118] (8)

[0119] Regarding the flow direction, the second-order upwind pattern is:

[0120] (9)

[0121] in, For the first The flux of the flow field within the basic grid cell is the TVD scheme discretization result of the region with shock waves. For the flow direction in the global coordinate system, For the sign of differentiation, for The derivative, The length of the basic unit of the adjacent grid. For the first Flux of the flow field within the basic grid cell For the first Flux of the flow field within the basic grid cell;

[0122] When the flow direction of the flow field is opposite to that from the first Mesh basic unit to the th When the basic grid cells are oriented in the same direction, if the shock wave appears at the th... Mesh basic unit and the first Between the basic grid units, then the first Flux of the flow field within the basic grid cell and the Flux of the flow field within the basic grid cell All will be affected by the shock wave;

[0123] When the flow direction of the flow field is opposite to that from the first Mesh basic unit to the th When the basic grid cells are oriented in opposite directions, if the shock wave appears at the th... Mesh basic unit and the first Between the basic grid units, then the first Flux of the flow field within the basic grid cell and the Flux of the flow field within the basic grid cell All will be affected by the shock wave;

[0124] Based on the width of the shock region, the space grid of the transonic vehicle is divided into shock-containing regions; the remaining part is the shockless region.

[0125] This application uses a second-order upwind pattern as an example, with a template width of... k The value is 3; if the shock wave occurs at the th... Mesh basic unit and the first Between the basic grid units, then and Both will be affected by the shock wave. Considering symmetry, if the flow direction (or characteristic direction) changes, the other side will be affected. and They will also be affected by the shock wave; therefore, a total of 4 grid points will be affected by the shock wave. . Figure 4 A schematic diagram of the shock wave and its affected area is provided. The area where the shock wave is present refers to... Figure 4 The area affected by the shock wave.

[0126] This application also provides a transonic flow numerical simulation system to implement the above-described method, which includes:

[0127] The initialization module is used to generate a spatial mesh based on the geometry of the transonic vehicle, set the calculation conditions, and provide an initial flow field with a Mach number less than a preset Mach number to initiate numerical calculations. The spatial mesh includes multiple mesh points or multiple mesh cells. The calculation conditions include incoming flow velocity, direction, Mach number, temperature, Reynolds number, density, pressure, and governing equations. The governing equations include the Euler equations or the Navier-Stokes equations.

[0128] The first calculation module is used to calculate the Mach number in the flow field;

[0129] The judgment module is used to determine whether there is a region in the flow field with a Mach number greater than a preset value based on the calculated Mach number. If it does not exist, it means that the entire flow field is a subsonic region and belongs to a shock wave-free region, and jumps to the second calculation module. If it exists, there is a supersonic region, and enters the region division module.

[0130] The region division module is used to determine whether there is a shock wave between adjacent grid points or unstructured grid cells. If a shock wave exists, it divides the region into a shock wave region and a region without a shock wave.

[0131] The second calculation module is used to discretize the spatial terms of the control equations using the TVD scheme for the defined shock wave region, and obtain the TVD scheme discretization result of the shock wave region; for the region determined to be without shock wave or the defined without shock wave region, the spatial terms of the control equations are discretized using the linear numerical scheme, and the linear scheme discretization result of the without shock wave region is obtained.

[0132] The flow field update module is used to update the flow field using a time-progression method based on the TVD format discretization results in the shock wave region and the linear format discretization results in the shock wave-free region.

[0133] The simulation result output module is used to determine whether the residuals have converged. If the residuals have not converged, the system jumps to the first calculation module and performs the loop calculation again. If the residuals have converged, the simulation results of the transonic flow are output. The simulation results include: shock wave region division information and converged flow field core parameters. The flow field core parameters include Mach number, density, velocity, temperature, and pressure. The residuals are the sum of iterative differences of the physical quantities of the entire flow field obtained by solving the governing equations. The flow field physical quantities include density, velocity, temperature, and pressure.

[0134] This application also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the computer program, when executed by the processor, implements the methods described in the above embodiments.

[0135] This application also provides a computer-readable storage medium, which includes a computer program or instructions that, when executed on a computer, cause the computer to perform the methods described in the above embodiments.

[0136] Comprehensive test:

[0137] The method proposed in this invention was tested using the Rae-2822 airfoil.

[0138] Step 01: Generate as follows Figure 2 The grid shown has 361×83 grid points. The Mach number of the incoming flow field is set to 0.734, the angle of attack is 2.84°, the Reynolds number (6.5 million) based on the airfoil chord length is set to 1, the dimensionless incoming flow velocity is set to 1, the temperature is set to 1, the viscosity coefficient is set to 1, the governing equation is the Reynolds-averaged Navier-Stokes equation, and the SA turbulence model is adopted.

[0139] Step 02: Give the uniform flow field with a Mach number of 0.5.

[0140] Step 03: Calculate the Mach number in the flow field.

[0141] Step 04: Based on the calculation results of Step 03, determine whether there is a region in the flow field with a Mach number greater than 1. If not, it means that the entire flow field is a subsonic region and belongs to a shock wave-free region. Proceed directly to Step 07.

[0142] Step 05: Determine and divide the regions with / without shock waves.

[0143] Step 06: Perform calculations on the region with shock waves, and use the TVD scheme to discretize the spatial terms of the control equations.

[0144] Step 07: Perform calculations for the shock-free region, using a linear numerical scheme to discretize the spatial terms of the control equations.

[0145] Step 08: Update the flow field using a time-progression method.

[0146] Step 09: Determine if the residuals have converged. A standard method can be used. If the residuals have not converged, iterate through steps 03 to 09 until the residual in step 09 is less than a set value (which can be 0.0001). Then automatically jump to the last step (step 10). The linear numerical scheme used during iteration is a second-order upwind scheme, the TVD scheme is an NND scheme, and the time-progression method is the LU-SUS method. If the residuals have converged, jump to step 10 and output the calculation results.

[0147] Step 10: Output the numerical simulation results. The numerical simulation ends.

[0148] Figure 2 The display shows a two-dimensional airfoil and the spatial mesh generated around it. Each spatial mesh has corresponding x and y coordinates. The corresponding spatial coordinates can be found by the mesh index to determine its location. x and y represent the flow direction and normal direction in the global coordinate system (two-dimensional), respectively.

[0149] Figure 5 It is based on Figure 2 The spatial pressure flow field cloud map is calculated using a spatial grid and the method of this application. P represents pressure, and the larger the number in the legend, the greater the pressure at the corresponding location.

[0150] Figure 6 The distribution of Mach number in the spatial flow field is shown, clearly illustrating the supersonic region. MA represents Mach number, with subsonic regions represented in white and supersonic regions shown in other colors. The area enclosed by the dashed line is the shock wave-affected region (the region with shock waves).

[0151] This application presents the complete process of solving transonic flow field partition coupling, the core of which is shock wave identification, shock wave influence region division and partition hybrid simulation (the region without shock wave adopts the linear numerical format, and the region with shock wave adopts the TVD format).

[0152] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of the claims of this application.

Claims

1. A numerical simulation method for transonic flow, characterized in that, include: Step 1: Generate a spatial mesh based on the geometry of the transonic vehicle, set the calculation conditions, and provide an initial flow field with a Mach number less than the preset Mach number; The spatial grid comprises multiple grid points or multiple grid cells; the calculation conditions include incoming flow velocity, direction, Mach number, temperature, Reynolds number, density, pressure, and governing equations; the governing equations include the Euler equations or the Navier-Stokes equations; Step 2: Calculate the Mach number in the flow field; Step 3: Based on the Mach number calculated in Step 2, determine whether there is a region in the flow field where the Mach number is greater than the preset value; if not, it means that the entire flow field is in the subsonic region and belongs to the shock wave-free region, and jump to Step 5; if it exists, there is a supersonic region, and proceed to Step 4. Step 4: Determine whether there is a shock wave between adjacent grid points or unstructured grid cells. If there is a shock wave, divide the area into a shock wave region and a non-shock wave region. Step 5: For the shock-prone regions identified in Step 4, the spatial terms of the control equations are discretized using the TVD scheme to obtain the TVD scheme discretization results for the shock-prone regions; for the shock-free regions identified in Step 3 or the shock-free regions identified in Step 4, the spatial terms of the control equations are discretized using a linear numerical scheme to obtain the linear scheme discretization results for the shock-free regions. Step 6: Update the flow field using the time-progression method based on the TVD scheme discretization results in the shock wave region and the linear scheme discretization results in the shock wave-free region; Step 7: Determine if the residuals have converged; if the residuals have not converged, jump to step 2 and recalculate the loop. If the residual converges, the simulation results of the transonic flow are output; the simulation results include: shock wave region division information, and converged flow field core parameters; the flow field core parameters include Mach number, density, velocity, temperature, and pressure; the residual is the sum of iterative differences of the physical quantities of the entire flow field obtained by solving the governing equations; the flow field physical quantities include density, velocity, temperature, and pressure; Step 4 includes: If the sound velocity in the flow field within adjacent grid points or unstructured grid cells is equal, then there is no shock wave between adjacent grid points or unstructured grid cells. Otherwise, calculate the Mach number between adjacent grid points or unstructured grid cells and match it with the Mach number in the gradient direction of the sound velocity. Based on the matching result, determine whether there is a shock wave between adjacent grid points or unstructured grid cells. The calculation of the Mach number between adjacent grid points or unstructured grid cells includes: If the first The sound velocity in the flow field within the basic grid cell is less than that of the first cell. The sound velocity of the flow field within the basic grid cell is then determined with reference to the shock front. The basic grid cell is located on one side of the shock front, corresponding to the first cell before the shock wave appears. The basic grid unit is located on the other side of the shock front, corresponding to the appearance of the shock wave; when the spatial grid is a structured grid, the first... The basic unit of the grid is the first Grid point, the first The basic unit of the grid is the first Grid points; when the spatial grid is an unstructured grid, the first The basic unit of the grid is the first Grid cell, the first The basic unit of the grid is the first Grid cells; Establish a local coordinate system, with its origin at a point on the shock front. The axis is parallel to the tangent at that point. The axis is perpendicular to the tangent at that point. shaft and shaft and The plane formed by the axes is perpendicular; Fixing the local coordinate system on the shock front, along the normal to the shock front, the... The Mach number of the flow field within the basic grid cell is The components on the axis are , No. The Mach number of the flow field within the basic grid cell is The components on the axis are Based on the Rankine-Yugonniu shock wave relationship, the following equation is obtained: (1) in, It is the specific heat ratio of gases. The temperature of the flow field before the shock wave appears. The temperature of the flow field after the shock wave appears; Temperature of the flow field before the shock wave appears Temperature of the flow field after the shock wave appears It is known that the time before the shock wave appears can be obtained by formula (1). ; The following formula is used to obtain the first... The basic unit of the grid corresponds to : (2)。 2. The method according to claim 1, characterized in that, Calculating the Mach number in the gradient direction of the sound velocity includes: The Mach number in the gradient direction of the speed of sound is calculated using the following formula: ， (3) in, Let be the component of the Mach number before the shock wave along the gradient direction of the sound speed. This represents the component of the Mach number following the shock wave along the gradient direction of the sound velocity. Let be the component of the velocity preceding the shock wave along the gradient of the speed of sound. Let be the component of the velocity following the shock wave along the gradient of the sound speed. For the first The sound velocity in the flow field within the basic grid cell. For the first The velocity of sound in the flow field within the basic grid cell.

3. The method according to claim 2, characterized in that, The gradient of sound velocity in the supersonic region is calculated using the following formula: (4) Where c is the speed of sound in the supersonic flow field. , , These correspond to the unit basis vectors on the x-axis, y-axis, and z-axis, respectively, and the directions of the unit basis vectors are consistent with the positive directions of the coordinate axes. Gradient symbol; and The expressions are as follows: (5) (6) in, , , These represent the flow field velocities in the direction of flow, normal direction, and spanwise direction before the shock wave appears. , , These represent the flow field velocities in the direction of flow, normal direction, and spanwise direction after the shock wave appears; The x-axis of the global coordinate system represents the flow direction; The y-axis of the global coordinate system represents the normal direction. The z-axis of the global coordinate system represents the span. When the global coordinate system is two-dimensional... and The values ​​of are all 0; the origin of the global coordinate system is a point on the leading edge of the transonic vehicle's geometry.

4. The method according to claim 2, characterized in that, The method involves matching the Mach number along the gradient direction of the sound velocity, and determining, based on the matching result, whether a shock wave exists between adjacent grid points or unstructured grid cells, including: pass , , , The degree of matching between them determines the first Mesh basic unit and the first Are there shock waves between the basic grid cells? If the first Mesh basic unit and the first If the Mach number between the basic grid elements satisfies formula (7), then the... Mesh basic unit and the first Shock waves exist between the basic grid cells; otherwise, the first Mesh basic unit and the first There are no shock waves between the basic grid cells; (7) in, It is a positive number.

5. The method according to claim 2, characterized in that, The division of the shock wave region and the non-shock wave region includes: The size of the shock region is related to the width of the grid template in the linear numerical format; Let the width of the mesh template be k, and the width of the shock wave region be k. for: (8) Regarding the flow direction, the second-order upwind pattern is: (9) in, For the first The flux of the flow field within the basic grid cell is the TVD scheme discretization result of the region with shock waves. For the flow direction in the global coordinate system, For the sign of differentiation, for The derivative of The length of the basic unit of the adjacent grid. For the first Flux of the flow field within the basic grid cell For the first Flux of the flow field within the basic grid cell; When the flow direction of the flow field is opposite to that from the first Mesh basic unit to the th When the basic grid cells are oriented in the same direction, if the shock wave appears at the th... Mesh basic unit and the first Between the basic grid units, then the first Flux of the flow field within the basic grid cell and the Flux of the flow field within the basic grid cell All will be affected by the shock wave; When the flow direction of the flow field is opposite to that from the first Mesh basic unit to the th When the basic grid cells are oriented in opposite directions, if the shock wave appears at the th... Mesh basic unit and the first Between the basic grid units, then the first Flux of the flow field within the basic grid cell and the Flux of the flow field within the basic grid cell All will be affected by the shock wave; Based on the width of the shock region, the space grid of the transonic vehicle is divided into shock-containing regions; the remaining part is the shockless region.

6. A transonic flow numerical simulation system, implementing the method described in any one of claims 1-5, characterized in that, include: The initialization module is used to generate a spatial mesh based on the geometry of the transonic vehicle, set the calculation conditions, and provide an initial flow field with a Mach number less than a preset Mach number. The spatial grid comprises multiple grid points or multiple grid cells; the calculation conditions include incoming flow velocity, direction, Mach number, temperature, Reynolds number, density, pressure, and governing equations; the governing equations include the Euler equations or the Navier-Stokes equations; The first calculation module is used to calculate the Mach number in the flow field; The judgment module is used to determine whether there is a region in the flow field with a Mach number greater than a preset value based on the calculated Mach number. If it does not exist, it means that the entire flow field is in the subsonic region, which is a shock wave-free region, and jumps to the second calculation module; if it exists, there is a supersonic region, and enters the region division module. The default value is a floating-point number; The region division module is used to determine whether there is a shock wave between adjacent grid points or unstructured grid cells. If a shock wave exists, it divides the region into a shock wave region and a region without a shock wave. The second calculation module is used to discretize the spatial terms of the control equations using the TVD scheme for the defined shock wave region, and obtain the TVD scheme discretization result of the shock wave region; for the region determined to be without shock wave or the defined without shock wave region, the spatial terms of the control equations are discretized using the linear numerical scheme, and the linear scheme discretization result of the without shock wave region is obtained. The flow field update module is used to update the flow field using a time-progression method based on the TVD format discretization results in the shock wave region and the linear format discretization results in the shock wave-free region. The simulation results output module is used to determine whether the residuals have converged; if the residuals have not converged, it jumps to the first calculation module and performs the loop calculation again. If the residual converges, the simulation results of the transonic flow are output; the simulation results include: shock wave region division information and converged flow field core parameters; the flow field core parameters include Mach number, density, velocity, temperature and pressure; the residual is the sum of iterative differences of the physical quantities of the entire flow field obtained by solving the governing equations; the flow field physical quantities include density, velocity, temperature and pressure.

7. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the computer program is executed by the processor, it implements the method of any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a computer program or instructions that, when executed on a computer, cause the computer to perform the method of any one of claims 1-5.

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