An efficient wide-rate domain format construction method based on algebraic form

Abstract

The present invention relates to the field of aerospace computational fluid dynamics technology, and discloses an efficient wide-speed domain format construction method based on algebraic form, including: generating a simulation discrete grid for the aerospace aircraft configuration to be calculated; decomposing the control equation flux passing through the discrete grid unit into convective flux and viscous flux; discretizing the convective flux using the HLLE++ format, and converting it into a combination of the left and right unit flux means and the dissipative term; decomposing the dissipative term into a combination of multiple groups of vectors, and decomposing each group of vectors into a product combination of HLLE++ format characteristic root terms, density terms, and velocity terms; integrating the convective flux into algebraic operations; iteratively solving the control equation to obtain the flow field information of each discrete grid unit. The present invention can solve the problems of low calculation efficiency and poor scalability of the existing HLLE++ construction, and has great application prospects in wide-speed domain multi-body separation, aircraft-missile separation, and numerical simulation of variant aircraft.

Description

Technical Field

[0001] The present invention relates to the technical field of aerospace computational fluid dynamics, and in particular to a highly efficient wide-speed domain format construction method based on algebraic form. Background Art

[0002] Numerical format is the foundation and soul of numerical simulation. HLLE++ format is a new convective flux discretization format developed in recent years. It avoids non-physical solutions such as the "ruby" phenomenon and the "step" behind the wave when capturing high-speed strong shock waves, while maintaining the low numerical dissipation characteristics in the smooth area. It can be well applied to high-speed multi-body separation, wide-domain variant aircraft flow field equations and adjoint equations, and is a very promising wide-speed domain numerical format.

[0003] At present, when constructing the HLLE++ format, its flux matrix is ​​usually written as the multiplication of three matrices. Although this method can realize the high-fidelity characteristics of HLLE++, this matrix-based HLLE++ format construction method brings two problems. First, when calculating convective flux, the computational efficiency of the matrix form is low. On the one hand, the operation of large matrices is relatively slow, and on the other hand, matrix operations occupy a large amount of computer memory, which will further reduce the computational efficiency. Secondly, in the gradient solution process, it is necessary to further calculate the partial derivatives of the inviscid flux convection field conservation variables. However, the flux matrix in the HLLE++ format is currently in the form of the multiplication of three matrices. Its own expression is very complex, and its partial derivative is even more complex. It is necessary to process the cross-derivative of multiple matrices. The complexity and difficulty of partial derivatives of convection field conservation variables are relatively large, and the scalability of the format is poor.

[0004] The paper "Application of HLLE++ Format in High Mach Number Cavity Flow Simulation" established an HLLE++ calculation method based on unstructured hybrid grids and applied it to the numerical simulation of high Mach number cavity flow. However, it still used the matrix form of HLLE++ format construction method, which has relatively low calculation efficiency and poor scalability of the format. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes an efficient wide-speed domain format construction method based on algebraic form, which decomposes the convection flux matrix into a combination of characteristic root terms, density terms and velocity terms, and improves the complex matrix properties into a simple algebraic form, thereby solving the problems of low computational efficiency and poor scalability of the original HLLE++ construction.

[0006] The technical solution adopted by the present invention is as follows:

[0007] An efficient wide-rate domain format construction method based on algebraic form, comprising:

[0008] For an aerospace vehicle configuration to be calculated, a simulation discrete grid is generated, wherein the simulation discrete grid includes a plurality of discrete grid units;

[0009] Decomposing the control equation flux through the discrete grid cells into a convective flux and a viscous flux;

[0010] The convective flux is discretized in HLLE++ format and converted into a combination of the left and right unit flux means and the dissipation term in HLLE++ format; the dissipation term in HLLE++ format is decomposed into a combination of multiple groups of five-dimensional vectors, and each group of five-dimensional vectors is decomposed into a product combination of characteristic root terms, density terms, and velocity terms in HLLE++ format; the convective flux is integrated into algebraic operations of addition, subtraction, multiplication, and division of characteristic root terms, density terms, and velocity terms in HLLE++ format;

[0011] The control equations are solved iteratively to obtain the flow field information of each discrete grid unit.

[0012] Furthermore, the dissipation term obtained by discretizing and transforming the convective flux includes: the product of the difference between the conservation variables of the left and right flow fields and the Jacobian matrix of the convective flux in the HLLE++ format.

[0013] Furthermore, the calculation method of the flow field conservation variable includes:

[0014]

[0015] in, is the flow field conservation variable, ρ is the density, u , v , w are the velocity components in three directions, E For the total energy.

[0016] Furthermore, the characteristic root terms obtained by decomposing the dissipation terms include relevant parameters of the characteristic roots in the HLLE++ format, the density terms include density, pressure and sound speed, and the velocity terms include velocity, sound speed, enthalpy and dynamic pressure.

[0017] Furthermore, the calculation method of the HLLE++ format characteristic root includes:

[0018]

[0019] in, is the characteristic root of HLLE++ format, is the characteristic root of HLLE+ format, is the characteristic root of Roe format modified by Harten entropy, The switch function is in HLLE++ format:

[0020]

[0021] in, is the hyperbolic tangent function, For the shock wave detector:

[0022]

[0023] in, V is the inverter speed, is the speed of sound, For pressure, is the pressure gradient, is the volume of the control body.

[0024] Furthermore, decomposing the dissipative term into a combination of multiple groups of vectors includes: solving the loosely coupled flow field equation and the turbulence equation, and decomposing the dissipative term in the HLLE++ format into the cumulative sum of five groups of five-dimensional vectors.

[0025] Furthermore, the grid form of the simulation discrete grid includes: structured grid, unstructured grid, Cartesian grid or hybrid grid.

[0026] Furthermore, the discretization method of the viscous flux includes: a central difference method.

[0027] Furthermore, the control equation includes: a Reynolds average equation in an integral form.

[0028] Furthermore, the flow field information includes: density, velocity and pressure of each discrete grid unit.

[0029] The beneficial effects of the present invention are:

[0030] 1. At present, when constructing the HLLE++ format, its flux matrix is ​​usually written as the multiplication of three matrices, and the dimension of each matrix is ​​5×5. During iterative calculation, each grid cell needs to apply for the memory of multiple matrices, and each processor needs to calculate tens of thousands of grid cells at the same time, which consumes a lot of memory. The present invention proposes an efficient wide-speed domain format construction method based on algebraic form, which transforms the complex matrix form into algebraic operations of eigenvalue terms, density terms, and velocity terms. The dimension of each term is only 5×1, which greatly reduces the system memory consumption.

[0031] 2. The traditional matrix-based HLLE++ format involves complex operations of multiple large matrices during iterative calculations, and has low calculation efficiency. The present invention converts the matrix form into algebraic operations, and the single-step calculation efficiency is improved by about 50%.

[0032] 3. In the process of gradient solution, it is necessary to further calculate the partial derivative of the inviscid flux on the conservation variables of the flow field. However, the expression of the HLLE++ format in the matrix form is very complicated, and the partial derivative is even more complicated. It is necessary to process the cross-derivative of multiple matrices, and the complexity and difficulty of partial derivative of the conservation variables of the flow field are relatively large. The present invention converts the matrix form into algebraic operations of addition, subtraction, multiplication and division, which greatly facilitates the calculation of the partial derivative of the inviscid flux on the conservation variables of the flow field in the gradient solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of a method for constructing a high-efficiency wide-speed domain format based on algebraic form according to the present invention.

[0034] Figure 2 It is an unstructured hybrid grid diagram of a symmetric double-cone vehicle.

[0035] Figure 3 It is the streamline diagram of a symmetrical double-cone aircraft.

[0036] Figure 4 This is a comparison chart of the efficiency of the HLLE++ format matrix form and algebraic form. DETAILED DESCRIPTION

[0037] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, the specific implementation methods of the present invention are now described. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the embodiments described are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0038] Example 1

[0039] like Figure 1 As shown, this embodiment provides an efficient wide-speed domain format construction method based on algebraic form, including: generating a simulation discrete grid for an aerospace vehicle configuration to be calculated, the simulation discrete grid including a plurality of discrete grid units; decomposing the control equation flux passing through the discrete grid unit into a convective flux and a viscous flux; discretizing the convective flux using the HLLE++ format, and converting it into a combination of the mean of the left and right unit fluxes and the dissipation term in the HLLE++ format; decomposing the dissipation term in the HLLE++ format into a combination of multiple groups of five-dimensional vectors, and decomposing each group of five-dimensional vectors into a product combination of characteristic root terms, density terms, and velocity terms in the HLLE++ format; integrating the convective flux into algebraic operations of addition, subtraction, multiplication, and division of characteristic root terms, density terms, and velocity terms in the HLLE++ format; iteratively solving the control equation to obtain the flow field information of each discrete grid unit.

[0040] like Figure 2 As shown, taking a symmetrical double-cone aircraft as an example, the efficient wide-speed domain format construction method of this embodiment is described in detail, which can be implemented by the following steps:

[0041] Step 1: Generate a simulation discrete grid for the symmetrical double-cone aircraft configuration to be calculated. Preferably, the simulation discrete grid used in this embodiment is an unstructured hybrid grid.

[0042] Step 2: The control equation used in this embodiment is the Reynolds-averaged Navier-Stokes (NS) equation. The control equation flux passing through the discrete grid unit is decomposed into convective flux and viscous flux. For three-dimensional steady compressible flow, the conservation form of the Reynolds-averaged equation can be written in the following integral form:

[0043]

[0044] in, represents the volume of the control volume, represents the area of ​​the closed surface of the control volume, is the virtual time quantity, is the flow field conservation variable, is the convective flux, is the viscous flux, S represents the area of ​​each face of the control volume. The discretization method of the viscous flux is the central difference format, and the flow field conservation variable for:

[0045]

[0046] in, ρ is the density, u , v , w are the velocity components in three directions, E For the total energy.

[0047] Step 3: Discretize the convective flux in step 2 using the HLLE++ format and write it as follows:

[0048]

[0049] in, is the convective flux in HLLE++ format, is the flux calculated using the left-hand element, is the flux calculated using the right-hand unit, is the right eigenvector of the Roe average Jacobian, is the difference between the left and right conserved variables. The coefficients of the projection, is the characteristic root in HLLE++ format and can be written as:

[0050]

[0051] in, is the characteristic root of HLLE++ format, is the characteristic root of HLLE+ format, is the characteristic root of Roe format modified by Harten entropy, The switch function is in HLLE++ format:

[0052]

[0053] in, is the hyperbolic tangent function, For the shock wave detector:

[0054]

[0055] in, V is the inverter speed, is the speed of sound, For pressure, is the pressure gradient, is the volume of the control body.

[0056] Step 4: Write the convective flux in HLLE++ format as a combination of the mean of the left and right unit fluxes and the dissipation term, where the dissipation term is the product of the difference between the conservation variables of the left and right flow fields and the Jacobian matrix of the convective flux:

[0057]

[0058] Among them, the subscript L represents the left unit, and the subscript R represents the right unit. and Conserved variables representing left and right states; represents the Jacobian matrix of the convection flux, the subscript I+1 / 2 represents the interface between the left and right units, represents the Jacobian matrix of convection on the interface between the left and right units.

[0059] Currently, when constructing the HLLE++ format, its flux matrix is ​​usually written as the multiplication of three matrices:

[0060]

[0061] in, and are the left and right eigenvectors of the Roe mean flux Jacobian, is a diagonal matrix of eigenvalues. The specific expansion form of this matrix form is not only very complex in expression, but also has two problems. First, in convection calculations, the computational efficiency of the matrix form is low and it also takes up a lot of computer memory. Secondly, in the gradient solution process, it is necessary to further calculate the partial derivatives of the conservation variables of the inviscid flux convection field. The expression of this matrix form itself is very complex, and the partial derivatives are even more complex. It is necessary to process the cross-derivatives of multiple matrices. The complexity and difficulty of finding the partial derivatives of the conservation variables of the convection field are relatively large, and the scalability of the format is poor.

[0062] Step 5: Decompose the dissipative term in HLLE++ format in step 4 into five groups of cumulative combinations of five-dimensional vectors:

[0063]

[0064] in, is the vector associated with the characteristic root of HLLE++ format, and its specific form is:

[0065]

[0066] in, is the characteristic root in HLLE++ format, is the density, is the pressure, u, v, w are the velocities in the x, y, and z directions respectively, c is the speed of sound, is the sum of squares of velocities, V is the inversion speed, H is the enthalpy, , , are the unit normal vectors in the x, y, and z directions respectively, is the difference between the left and right units, is the Roe average variable.

[0067] Step 6: Each set of five-dimensional vectors in step 5 ( ) is decomposed into HLLE++ format characteristic root terms ( ), density term ( ), the product combination of speed terms ( ), where the characteristic root term is the relevant parameter of the characteristic root in HLLE++ format, the density term is related to density, pressure and sound speed, and the velocity term is related to velocity, sound speed, enthalpy and dynamic pressure. The specific decomposition process is:

[0068] Characteristic root term:

[0069]

[0070] Density term:

[0071]

[0072] Speed ​​Item:

[0073]

[0074] The definition of each parameter is the same as in step 5.

[0075] Step 7: Integrate the convective flux in HLLE++ format into algebraic operations of addition, subtraction, multiplication and division of characteristic root terms, density terms and velocity terms in HLLE++ format:

[0076]

[0077] Step 8: Iteratively solve the integral form of the Reynolds-averaged Navier-Stokes (RANS) equation to obtain the flow field information of each discrete grid cell, including the density, velocity and pressure of each grid cell. Figure 3 Shown is the streamline diagram calculated for a symmetric double-cone vehicle, showing typical high-speed shock wave characteristics.

[0078] The present invention proposes an efficient wide-speed domain format construction method based on algebraic form, which transforms the complex matrix form into algebraic operations of eigenvalue terms, density terms, and speed terms. From the perspective of memory consumption, only the memory of the vector needs to be applied, which greatly reduces the system memory consumption.

[0079] In order to more accurately compare the computational efficiency before and after the HLLE++ format improvement, Figure 4 The time taken for 1000 iterations of HLLE++ inviscid flux calculation is given. By comparison, it is found that the present invention converts the matrix form into algebraic operations, and the single-step calculation efficiency is improved by about 50%. In the gradient solution process, the partial derivatives of the inviscid flux on the conservation variables of the flow field need to be further calculated. The present invention converts the matrix form into algebraic operations of addition, subtraction, multiplication and division, which greatly facilitates the calculation of the partial derivatives of the inviscid flux on the conservation variables of the flow field in the gradient solution.

[0080] Example 2

[0081] This embodiment is based on embodiment 1:

[0082] This embodiment provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the algebraic form-based efficient wide-speed domain format construction method of embodiment 1 are implemented. The computer program may be in source code form, object code form, executable file, or some intermediate form.

[0083] Example 3

[0084] This embodiment is based on embodiment 1:

[0085] The present embodiment provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the algebraic-based efficient wide-speed domain format construction method of Embodiment 1. The computer program may be in source code form, object code form, executable file, or some intermediate form, etc. The storage medium includes: any entity or device capable of carrying computer program code, recording medium, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the content contained in the storage medium may be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the storage medium does not include electric carrier signals and telecommunication signals.

[0086] It should be noted that, for the aforementioned method embodiments, for the sake of simplicity of description, they are expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the order of the actions described, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

Claims

1. An efficient wide-rate domain format construction method based on algebraic form, characterized in that: include: For an aerospace vehicle configuration to be calculated, a simulation discrete grid is generated, wherein the simulation discrete grid includes a plurality of discrete grid units; Decomposing the control equation flux through the discrete grid cells into a convective flux and a viscous flux; The convective flux is discretized in HLLE++ format and converted into a combination of the left and right unit flux means and the dissipation term in HLLE++ format; the dissipation term in HLLE++ format is decomposed into a combination of multiple groups of five-dimensional vectors, and each group of five-dimensional vectors is decomposed into a product combination of characteristic root terms, density terms, and velocity terms in HLLE++ format; the convective flux is integrated into algebraic operations of addition, subtraction, multiplication, and division of characteristic root terms, density terms, and velocity terms in HLLE++ format; Iteratively solve the control equations to obtain the flow field information of each discrete grid unit; The dissipation term in the HLLE++ format is decomposed into a combination of multiple groups of five-dimensional vectors, and each group of five-dimensional vectors is decomposed into a product combination of characteristic root terms, density terms, and velocity terms in the HLLE++ format; the convective flux is integrated into algebraic operations of addition, subtraction, multiplication, and division of characteristic root terms, density terms, and velocity terms in the HLLE++ format, including: Decompose the dissipative term in HLLE++ format into five groups of cumulative combinations of five-dimensional vectors: in, is the vector associated with the HLLE++ format characteristic root, and the expressions include: in, is the characteristic root in HLLE++ format, is the density, is the pressure, u, v, w are the velocities in the x, y, and z directions respectively, c is the speed of sound, is the sum of squares of velocities, V is the inversion speed, H is the enthalpy, , , are the unit normal vectors in the x, y, and z directions respectively, is the difference between the left and right units, is the Roe average variable; Each set of five-dimensional vectors ( ) is decomposed into HLLE++ format characteristic root terms , density term , product combination of velocity terms , where the characteristic root term is the relevant parameter of the characteristic root in HLLE++ format, the density term is related to density, pressure and sound velocity, and the velocity term is related to velocity, sound velocity, enthalpy and dynamic pressure. The decomposition process includes: Characteristic root term: Density term: Speed ​​Item: The convective flux in HLLE++ format is integrated into the algebraic operations of addition, subtraction, multiplication and division of the characteristic root term, density term and velocity term in HLLE++ format: 。 2. The method for constructing an efficient wide-speed domain format based on algebraic form according to claim 1, characterized in that: The dissipation term obtained by discretizing and transforming the convective flux includes: the product of the difference between the conservation variables of the left and right flow fields and the Jacobian matrix of the convective flux in the HLLE++ format.

3. The method for constructing an efficient wide-speed domain format based on algebraic form according to claim 2, characterized in that: The calculation method of the flow field conservation variable includes: in, is the flow field conservation variable, ρ is the density, u , v , w are the velocity components in three directions, E For the total energy.

4. The method for constructing an efficient wide-speed domain format based on algebraic form according to claim 1, characterized in that: The characteristic root terms decomposed from the dissipation terms include relevant parameters of the characteristic roots in the HLLE++ format, the density terms include algebraic operations of density, pressure and sound speed, and the velocity terms include algebraic operations of velocity, sound speed, enthalpy and dynamic pressure.

5. The method for constructing an efficient wide-speed domain format based on algebraic form according to claim 4, characterized in that: The calculation method of the HLLE++ format characteristic root includes: in, is the characteristic root of HLLE++ format, is the characteristic root of HLLE+ format, is the characteristic root of Roe format modified by Harten entropy, The switch function is in HLLE++ format: in, is the hyperbolic tangent function, For the shock wave detector: in, V is the inverter speed, is the speed of sound, For pressure, is the pressure gradient, is the volume of the control body.

6. The method for constructing an efficient wide-speed domain format based on algebraic form according to claim 1, characterized in that: The combination of decomposing the dissipative term into multiple groups of vectors includes: solving the loosely coupled flow field equation and the turbulence equation, and decomposing the dissipative term in the HLLE++ format into the cumulative sum of five groups of five-dimensional vectors.

7. The method for constructing an efficient wide-speed domain format based on algebraic form according to claim 1, characterized in that: The grid form of the simulation discrete grid includes: structured grid, unstructured grid, Cartesian grid or mixed grid.

8. The method for constructing an efficient wide-speed domain format based on algebraic form according to claim 1, characterized in that: The discretization method of the viscous flux includes: a central difference method.

9. The method for constructing an efficient wide-speed domain format based on algebraic form according to claim 1, characterized in that: The control equations include: Reynolds average equations in integral form.

10. The method for constructing an efficient wide-speed domain format based on algebraic form according to claim 1, characterized in that: The flow field information includes: density, velocity and pressure of each discrete grid unit.

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