A flow field analysis method for supersonic viscous fluid

Abstract

The present invention relates to a flow field analysis method for a supersonic viscous fluid, and belongs to the technical field of flow field analysis. The present invention performs external processing on the solution of linear weights so that the obtained linear weights are all positive numbers, thereby solving the problem that negative weights may appear in the linear weights of a WENO format based on a traditional central difference format, and improving the stability of the format. Secondly, by setting a Gaussian function, nonlinear weighting is performed on the inner derivatives in the viscosity numerical flux of the final nonlinear combination, thereby solving the problem of computational divergence existing in directly using a Lagrange interpolation function and calculating its derivative function, and enhancing the robustness of the flow field analysis method.

Description

Technical Field

[0001] The present invention relates to the technical field of flow field analysis, and in particular to a flow field analysis method for a supersonic viscous fluid. Background Art

[0002] Numerous flow problems in everyday life are closely related to the field of fluid mechanics, such as cars on the road, airplanes in the sky, and boats at sea. To achieve better flow performance, people can simulate the flow characteristics of these given scenarios through fluid mechanics. Based on the simulated flow characteristics, they can perform design and reverse engineering, ultimately obtaining design parameters that meet the requirements. Compared to experimental fluid dynamics, computational fluid dynamics offers the advantages of high efficiency, high precision, low cost, and experimental repeatability in certain extreme environments. It is currently widely used in both military and civilian fields.

[0003] In order to solve the viscosity term of the governing equation in fluid mechanics, the conventional central difference scheme is usually used to discretize the parameters. However, the traditional central difference format has the following problems when analyzing supersonic viscous flow problems: (1) Since the traditional central difference format needs to discretize the outer derivative first and then symmetrically discretize the inner derivative involved, the difference format with (2r) order format accuracy requires flow information from (4r+1) grid cell points. The excessive number of grid cell points makes it difficult to handle the boundary; (2) Supersonic viscous flow problems are usually accompanied by the appearance of strong shock waves and strong discontinuities, and the traditional central difference format numerically discretizes the inner derivative by directly constructing the Lagrangian interpolation function and calculating its derivative function. This discretization basis obviously does not meet the smoothness requirements of the interpolation function, and thus ultimately leads to poor robustness of the result, failure to converge or even collapse; (3) The WENO format (weighted essential non-oscillation) constructed based on the traditional central difference format will have negative linear weights. This feature also makes the constructed WENO format unstable, and eventually causes the system to crash.

[0004] Therefore, developing a flow field analysis method suitable for supersonic viscous fluids under the finite difference framework has important theoretical significance and practical application value. Summary of the Invention

[0005] In view of the above problems, the present invention provides a flow field analysis method for supersonic viscous fluids. Specifically, by externalizing the solution of linear weights, all obtained linear weights are positive, solving the problem of negative linear weights in the WENO format based on the traditional central difference format and improving the stability of the format. Secondly, by setting a Gaussian function, the internal derivatives of the final nonlinearly combined viscous numerical flux are nonlinearly weighted, solving the computational divergence problem that exists when directly using the Lagrange interpolation function and calculating its derivative function, and enhancing the robustness of the flow field analysis method.

[0006] The present invention provides a flow field analysis method for supersonic viscous fluid, which comprises the following steps:

[0007] Step 1: Generate a structured grid of the area to be analyzed of the flow field analysis object; initialize the function point values ​​on the grid cells according to the given initial boundary conditions to obtain the function value of each grid cell in the initial state;

[0008] Step 2: According to the viscosity numerical flux at the boundary of the target grid cell Determine the grid cells required for the discretization of the viscosity term in the control equation and define them as the large template S; divide the large template S into several small templates S of the same size m , m=0,1,2…,N, where N is the number of divided small templates and the number of grid cells on each small template is r; the reconstruction-based integral function is used to obtain the reconstructed viscosity numerical flux function on the large template and the small template respectively; the viscosity numerical flux on the target cell boundary on the large template and the small template is obtained;

[0009] Step 3: The numerical flux on the large template obtained in step 2 Numerical flux on a small template and the corresponding target cell boundary The linear weight d of each small template is obtained by the method of undetermined coefficients m ;

[0010] Step 4: Reconstruct the viscosity numerical flux function p of each small template based on step 2 m (x) Obtain the corresponding smoothing factor on the small template;

[0011] Step 5: Based on the linear weights d of each small template in step 3 m and the smoothing factor β from step 4 m , obtain the nonlinear weight ω on each small template m ;

[0012] Step 6: Based on the nonlinear weights on each small template and the target unit boundaries on each small template Viscous numerical flux on Get the final target cell boundary Viscous numerical flux on ;

[0013] Step 7: Repeat steps 2-6 to obtain the final target cell boundary Viscous numerical flux on

[0014]

[0015] Step 8: Use the WENO difference scheme to discretize the inviscid numerical flux corresponding to the final viscous numerical flux on the target unit boundary obtained in steps 6 and 7. The time derivatives of the conserved variables in the flow field are obtained by using the conservative semi-discrete format of the governing equations. The derivative of the conserved variable with respect to time in the convection field The variable values ​​in the flow field are obtained by advancing the solution in time.

[0016] Preferably, the object to be analyzed for flow field is a supersonic aircraft.

[0017] Preferably, the initial boundary conditions are supersonic far-field incoming flow conditions.

[0018] Preferably, the reconstruction-based integral function is used to obtain the reconstructed viscosity numerical flux function p(x) on the large template, which is expressed as:

[0019]

[0020] Among them, x represents the input parameter; x j represents the jth grid unit; G(u(x j ),u x (x j )) represents the viscosity term of the governing equation in the grid cell x in the corresponding template j Function value on u(x j ) represents the jth grid cell x j The function value of the independent variable on u x (x j ) represents the jth grid cell x j The derivative of the function of the independent variable on .

[0021] Preferably, based on the viscosity numerical flux function p(x) obtained in the above steps, the target unit boundary on the large template is obtained Viscous numerical flux on The expression is:

[0022]

[0023] Preferably, the reconstruction viscosity numerical flux function p of each small template is obtained by using the reconstruction-based integral function m (x), the expression is:

[0024]

[0025] Among them, x represents the input parameter; x j represents the jth grid unit; G(u(x j ),u x (x j )) represents the viscosity term of the governing equation in the grid cell x in the corresponding template j Function value on u(x j ) represents the jth grid cell x j The function value of the independent variable on u x (x j ) represents the jth grid cell x j The derivative of the function of the independent variable on .

[0026] Preferably, in step 3, the linear weight d of each small template m The expression is:

[0027]

[0028] Among them, d m represents the linear weight of the mth small template; Indicates that the large template S calculated in step 2 is at the boundary of the target unit The corresponding viscous numerical flux; Represents the small template S obtained by step 2 m In the target unit The corresponding viscous numerical flux.

[0029] Preferably, in step 4, the expression of the smoothing factor is:

[0030]

[0031] Among them, β m represents the smoothing factor of the mth small template; r represents the number of grid cells on the small template; xJ represents the coordinates of the center point of the Jth target cell discrete point; xJ+1 represents the coordinates of the center point of the J+1th target cell discrete point; It represents the l-th derivative of the flux function along the x-axis, where l = 1, 2, …, r; dx represents the integration of the x-th input parameter.

[0032] Preferably, the nonlinear weight ω on the small template m , the expression is:

[0033]

[0034] Among them, ω m Represents the nonlinear weight on the mth small template; Represents the nonlinear weight of the intermediate process; d m represents the linear weight of the mth small template; ε represents a small positive number to avoid the denominator being 0.

[0035] Preferably, the variable values ​​in the flow field obtained in step 8 are density, momentum in the x-direction, momentum in the y-direction, and total energy.

[0036] Compared with the prior art, the present invention has at least the following beneficial effects:

[0037] 1. The flow field analysis method for supersonic viscous fluids proposed in this paper proposes a WENO framework. In this WENO framework, the (2r)-order format accuracy only requires (2r+1) grid cells (where r is a natural number, such as when r=3, the sixth-order format accuracy requires 7 grid cells). Compared with the traditional central difference format, this can effectively reduce the number of grid cells required for format construction, thereby effectively reducing the difficulty of boundary processing.

[0038] 2. The flow field analysis method for supersonic viscous fluids of the present invention proposes a WENO framework. Under this WENO framework, all linear weights obtained are positive, which can effectively avoid the problem of negative linear weights that appear in the traditional WENO format based on central difference, and solve the problem of unstable results during flow field analysis.

[0039] 3. The present invention proposes a WENO framework for analyzing the flow field of supersonic viscous fluids. Within this framework, a Gaussian function is set to nonlinearly weight the derivative values ​​on the large and small templates, ultimately calculating the derivative value of the numerical flux in the expression. This effectively avoids the problem of computational divergence caused by directly performing Lagrangian interpolation on the large template and calculating its derivative function.

[0040] 4. The flow field analysis method of the supersonic viscous fluid of the present invention proposes a WENO framework, which is suitable for solving supersonic viscous flow problems, making the calculation less likely to diverge. While ensuring the accuracy of the calculation format, it enhances the robustness and stability of the calculation format, and has important application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Schematic diagram of the method of the present invention for discretizing grid units in one dimension;

[0042] Figure 2 This is a grid unit decomposition diagram of the method of the present invention in the two-dimensional Mach 2000 jet problem calculation area;

[0043] Figure 3 This is a density diagram of the flow field initialization state at time t=0.0 in an embodiment of the present invention;

[0044] Figure 4 This is a density diagram of the logarithmic function of the flow field calculated when t=0.001 in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. In addition, the present invention can also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited by the specific embodiments disclosed below.

[0046] A specific embodiment of the present invention, as Figures 1-4 , discloses a flow field analysis method for supersonic viscous fluid. First, the defined large template is divided into several corresponding small templates. Then, a reconstruction-based method is used on the large template and each small template to obtain the numerical flux expression defined at the unit center point. Based on these numerical flux expressions, the corresponding linear weights on different small templates can be obtained. In order to convert the linear weight into a nonlinear weight, the smoothing factor on the corresponding small template is obtained by integral expression, and the Lagrange interpolation function and its derivative function on the corresponding small template are constructed to obtain the derivative value on the smoothing factor, and finally the nonlinear weight can be obtained. For the derivative function on the nonlinearly weighted numerical flux, a Gaussian function is set to perform nonlinear weighting on the derivative value on the corresponding small template and the derivative value on the large template. Finally, the numerical flux value on the unit boundary can be obtained, and the solution is obtained by time advancement. The specific steps are as follows:

[0047] Step 1: Generate a structured grid of the area to be analyzed of the flow field analysis object; initialize the function point values ​​on the grid cells according to the given initial boundary conditions to obtain the function value of each grid cell in the initial state;

[0048] Optionally, the object to be analyzed for flow field is a supersonic aircraft.

[0049] Among them, the structured grid includes multiple grid units x j , the left boundary of the grid cell is The right edge of the grid cell is

[0050] Exemplarily, the initial boundary condition is a supersonic far-field incoming flow condition. According to the supersonic far-field incoming flow condition, the function point values ​​on the grid points can be initialized according to the position coordinate information of the grid cells.

[0051] Step 2: According to the viscosity numerical flux at the boundary of the target grid cell Determine the grid cells required for the discretization of the viscosity term G in the control equation to be solved, and define it as the large template S; divide the large template S into several small templates S of the same size m , m=0,1,2…,N, where N is the number of divided small templates and the number of grid cells on each small template is r; the reconstruction-based integral function is used to obtain the reconstructed viscosity numerical flux function on the large template and the small template respectively; the viscosity numerical flux on the boundary of the target cell on the large template and the small template is obtained.

[0052] Furthermore, the reconstruction-based integral function is used to obtain the reconstructed viscosity numerical flux function p(x) on the large template, which is expressed as:

[0053]

[0054] Among them, x represents the input parameter; x j represents the jth grid unit; G(u(x j ),u x (x j )) represents the viscosity term of the equation in the grid cell x in the corresponding template j The function value on the j ) and u x (x j ) composite composition; u(x j ) represents the jth grid cell x j The function value of the independent variable on u x (x j ) represents the jth grid cell x j The derivative value of the independent variable function on ; S represents the large template.

[0055] Furthermore, based on the viscosity numerical flux function p(x) obtained in the above steps, the target unit boundary on the large template is obtained. Viscous numerical flux on The expression is:

[0056]

[0057] Furthermore, the reconstruction-based integral function is used to obtain the reconstructed viscosity numerical flux function p of each small template. m (x), the expression is:

[0058]

[0059] Furthermore, the viscosity numerical flux function p obtained based on the above steps is m(x), get the target unit boundary on the small template Viscous numerical flux on The expression is:

[0060]

[0061] Step 3: The numerical flux on the large template obtained in step 2 Numerical flux on a small template and the corresponding target cell boundary The linear weight d of each small template is obtained by the method of undetermined coefficients m , the expression is:

[0062]

[0063] Among them, d m represents the linear weight of the mth small template; Indicates that the large template S calculated in step 2 is at the boundary of the target unit The corresponding viscous numerical flux; Represents the small template S obtained by step 2 m In the target unit The corresponding viscous numerical flux.

[0064] Step 4: Reconstruct the viscosity numerical flux function p of each small template based on step 2 m (x) Obtain the corresponding smoothing factor on the small template;

[0065] The expression of the smoothing factor is:

[0066]

[0067] Among them, β m Represents the smoothing factor of the mth small template, which is the viscosity numerical flux function p on the corresponding small template m The integral of the sum of squares of the derivative functions of each order of (x); r represents the number of grid cells on the small template; xJ represents the coordinates of the center point of the Jth target cell discrete point; xJ+1 represents the coordinates of the center point of the J+1th target cell discrete point; It means finding the l-order derivative of the flux function along the x-axis, where l = 1, 2, ... r; dx means integrating the x-th input parameter;

[0068] Among them, the smoothing factor β m is a series of point values ​​of the viscosity flux term G(u(x j ),u x (x j )) is a linear combination of u(x j ) and u x(x j ) composite composition, u(x j ) represents the value of the independent variable function on the j-th grid unit; u x (x j ) represents the derivative value of the independent variable function on the jth grid unit; where u(x j ) can be directly obtained through the flow field point value, and u x (x j ) then it is necessary to construct the Lagrange interpolation function on the small template and find its derivative function, and then calculate the corresponding point x=x j Substitute the coordinates of into the calculation to obtain;

[0069] Furthermore, the Lagrangian interpolation function of each small template is:

[0070]

[0071] Among them, l m,j (x) represents the jth Lagrange interpolation basis function on the mth small template; u(x j ) represents the center point x=x at the jth grid cell in the flow field. j The function value of the independent variable on ;

[0072] Furthermore, the derivative of the Lagrange interpolation function is:

[0073]

[0074] When the corresponding coordinate position x=x j When substituting into the derivative function of the above Lagrange interpolation function, we can get the corresponding derivative function value, that is, Indicates the derivative of the function along the x direction; the final smoothing factor β is obtained by combining the expression of the smoothing factor and the Lagrange interpolation of each small template m .

[0075] Furthermore, the flow field value includes the density, velocity, total energy, etc. of the object to be analyzed.

[0076] Step 5: Based on the linear weights d of each small template in step 3 m and the smoothing factor β from step 4 m , obtain the nonlinear weight ω on each small template m , the expression is:

[0077]

[0078] Among them, ω m Represents the nonlinear weight on the mth small template; Represents the nonlinear weight of the intermediate process; dm represents the linear weight of the mth small template; ε represents a small positive number to avoid the denominator being 0;

[0079] Preferably, ε=10 -6 .

[0080] Step 6: Based on the nonlinear weights on each small template and the target unit boundaries on each small template Viscous numerical flux on Get the final target cell boundary The specific expression of the viscous numerical flux on is:

[0081]

[0082] It can be understood that the viscous numerical fluxes on the target unit boundary include density, velocity, pressure, total energy and temperature.

[0083] Furthermore, the target cell boundary on the small template Viscous numerical flux on is a series of point values ​​of the viscosity flux term G(u(x j ),u x (x j )) is a linear combination of u(x j ) and u x (x j ) composite composition, u(x j ) represents the value of the independent variable function on the j-th grid unit; u x (x j ) represents the derivative value of the independent variable function on the jth grid unit; where u(x j ) can be directly obtained through the flow field point value, and u x (x j ) then it is necessary to construct the Lagrange interpolation function on the small template and find its derivative function, and then calculate the corresponding point x=x j Substitute the coordinates of into the calculation to obtain Then, by constructing the Lagrange interpolation function on the small template and finding its derivative function, and according to the corresponding point x=x j Substitute the coordinates of into the calculation to obtain

[0084] Furthermore, u x (x j ) is and The nonlinear weighted function value of is expressed as follows:

[0085]

[0086] in, is the nonlinear weight ω on the mth small template m With linear weight d m The ratio of Φ(θ m ) is a specific Gaussian function value, which is defined as:

[0087]

[0088] Wherein, e represents a natural constant, preferably, e is approximately equal to 2.71828;

[0089] Finally, the viscous numerical flux on the grid cell boundary can be calculated by using the conserved physical variable value u in the flow field

[0090] Step 7: Repeat steps 2-6 to obtain the final target cell boundary Viscous numerical flux on

[0091]

[0092] Step 8: Use the WENO difference scheme to discretize the inviscid numerical flux corresponding to the final viscous numerical flux on the template target unit boundary obtained in steps 6 and 7. The time derivatives of the conserved variables in the flow field are obtained by using the conservative semi-discrete format of the governing equations. The derivative of the conserved variable with respect to time in the convection field The variable values ​​in the flow field are obtained by advancing the solution in time.

[0093] The conservative semi-discrete format of the governing equation is expressed as:

[0094]

[0095] Among them, u j＝ u(x j ) represents the center point x=x at the jth grid cell in the flow field. j The function value of the independent variable on .

[0096] Then the derivative of the conserved variable in the flow field with respect to time is The variable values ​​in the flow field are obtained by advancing the solution in time using the third-order Runge-Kutta method.

[0097] Furthermore, variables in the flow field include density, momentum in the x-direction, momentum in the y-direction, total energy, and the like.

[0098] Exemplarily, the variables in the flow field include density ρ, velocity component u in the x-axis direction, velocity component v in the y-axis direction, pressure p, total energy E, and temperature T of the fluid.

[0099] The governing equation for solving the variable values ​​in the flow field is the two-dimensional Navier-Stokes equation, which is expressed as follows:

[0100]

[0101] Among them: U is the conserved variable to be solved, F1 and F2 (i.e. and ) is the inviscid term of the equation, G1 and G2 (i.e. and ) is the viscosity term of the equation; x represents the coordinate axis x; y represents the coordinate axis y.

[0102] Furthermore, U, F1, F2, G1, and G2 are defined as follows:

[0103]

[0104] Where τ is the stress variable and q is the heat flux, which is defined as:

[0105]

[0106] For the above two-dimensional Navier-Stokes equation, the corresponding ideal gas state equation is:

[0107]

[0108] Where ρ is the density, u and v are the velocity components in the x-axis and y-axis directions respectively, p is the pressure, E is the total energy, T is the temperature of the fluid, Pr is the corresponding Prandtl constant, and γ is the general heat flow constant, which is 1.4 for ideal gases.

[0109] Optionally, in the actual calculation process, the physical quantities to be solved are ρ, u, v, and p. For other physical quantities of interest, such as total energy E, temperature T, etc., they can be obtained by directly solving the state equation.

[0110] It should be noted that the flow field variables in the above steps represent each component of the conserved variables to be solved. In order to illustrate the effectiveness of the method proposed in the present invention, the above technical solution of the present invention is described in detail below through a specific embodiment, as follows:

[0111] Take the two-dimensional Mach 2000 jet problem as an example. This problem can be regarded as a simplified model of an aircraft engine nozzle. This is a numerical example with a Mach number of about 2000. The regional mesh is obtained as follows: Figure 2As shown. The compact robust WENO difference method proposed by the present invention for supersonic viscous flow problems is used to numerically discretize the viscous terms G1 and G2 in the equation. The specific simulation accuracy is a sixth-order precision discrete format. For this problem, the specific steps of this method are as follows:

[0112] (1) For this problem, we first determine the computational domain and initial boundary conditions for solving the problem. The computational domain of this problem is: This problem is a rectangular computational domain of [0,1]*[-0.25,0.25]. The computational domain is divided into structured grids, such as Figure 2 As shown; in the same dimensional direction, the calculation area can be divided into N mutually non-intersecting grid units, where The jth grid cell I j Defined as: and For unit I j The initial conditions of this problem are: in the initial state, density ρ = 0.5, velocity u = v = 0, and pressure p = 0.4127; the boundary conditions of this problem are: the right boundary, upper boundary, and lower boundary are outflow boundary conditions, and the left boundary is the inflow boundary condition. Specifically, when y∈[-0.05,0.05], density ρ = 5, velocity u = 800, v = 0, and pressure p = 0.4127. The rest are: density ρ = 5, velocity u = 0, v = 0, and pressure p = 0.4127.

[0113] (2) Flow field initialization: Based on the initial conditions given above, the flow field can be initialized directly according to the unknown points in the calculation area, and the flow field state information of the corresponding points at the initial moment can be obtained;

[0114] (3) Calculate the numerical flux expression on different templates: To perform a sixth-order compact central difference discretization on the viscosity term G1 in the equation and obtain the unit boundary The numerical flux on the first definition of a template S = {x j-2 ,x j-1 ,x j ,x j+1 ,x j+2 ,x j+3} and three small templates S m ={x j-2+m ,...,x j+1+m},m=0,1,2, such as Figure 1 As shown, a fifth-order polynomial is defined on the large template S: p(x)=a0+a1x+a2x 2 +a3x 3 +a4x 4 +a5x 5, where a0, a1, a2, a3, a4, a5 are unknown coefficients to be determined; to obtain these unknown coefficients, we can use the function implicitly defined on the template S Where j = {j-2, j-1, j, j+1, j+2, j+3} is the corresponding unit index on the template S. Substituting the polynomial into it can obtain a closed system of linear equations with five variables. Solving the system of equations can obtain the corresponding unknown coefficients a0, a1, a2, a3, a4, a5, and take the function p(x) The function value on the unit boundary can be obtained by Numerical flux expression on : Similarly, the same operation can be performed on the three small templates to obtain the numerical flux on the corresponding small templates:

[0115]

[0116] (4) Calculate the linear weight on the small template: In order to make the numerical flux on the small template weighted to the value on the large template, define the formula: The corresponding linear weight can be calculated as:

[0117]

[0118] (5) Calculate the smoothness factor on the small template: by integrating the expression The smoothing factor on the small template can be calculated. For the derivative function value involved in the smoothing factor, the Lagrange interpolation function can be directly constructed on the corresponding small template, its derivative function can be calculated, and the corresponding point value can be taken to obtain the result.

[0119] (6) Convert linear weights into nonlinear weights: by the expression

[0120] The nonlinear weight ω corresponding to different small templates can be calculated m ;

[0121] (7) Nonlinear weighting of the derivative function value on the small template: Definition For the derivative function in the numerical flux expression on the small template, the Gaussian function The derivative function value calculated by the small template and the derivative function value calculated by the large template are nonlinearly weighted. The specific expression is: Calculate in this way The values ​​of the derivatives involved;

[0122] (8) Calculate the viscosity numerical flux on the unit boundary: by the expression The final viscous numerical flux on the unit boundary can be calculated by nonlinear weighting. The viscous term G2 can be numerically discretized in a similar way.

[0123] (9) For the inviscid terms F1 and F2 in the equation, the weighted essential non-oscillation method can be used for discretization, and the inviscid numerical flux on the unit boundary can be obtained by calculation;

[0124] (10) Advancing the solution in time: The inviscid numerical flux and viscous numerical flux on the unit boundary are calculated through the above steps, that is, the spatial discretization has been completed, and then the solution can be advanced in time.

[0125] Furthermore, the time marching solution is performed by using the following third-order TVD Runge-Kutta method, which is expressed as:

[0126]

[0127] in, Unit I at time n j The point value on , Δt is the time step, Unit I at time n j The spatial discrete operator on , Unit I at time n+1 j The point value on the time can be pushed forward to the next moment by the above formula;

[0128] (11) Repeat steps (3) to (10) until the set calculation time is reached, and then the calculation results ρ, u, v, p can be output to complete the discrete solution of the algorithm. In this example, the logarithmic function density diagram of the Mach 2000 jet problem at time t = 0.001 is as follows Figure 3 shown.

[0129] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A flow field analysis method for supersonic viscous fluid, characterized in that: The specific steps are as follows: Step 1: Generate a structured grid of the area to be analyzed of the flow field analysis object; initialize the function point values ​​on the grid cells according to the given initial boundary conditions to obtain the function value of each grid cell in the initial state; Step 2: According to the viscosity numerical flux at the boundary of the target grid cell Determine the grid cells required for the discretization of the viscosity term in the control equation and define them as the large template S; divide the large template S into several small templates S of the same size m , m=0,1,2…,N, where N is the number of divided small templates and the number of grid cells on each small template is r; the reconstruction-based integral function is used to obtain the reconstructed viscosity numerical flux function on the large template and the small template respectively; the viscosity numerical flux on the target cell boundary on the large template and the small template is obtained; Step 3: The numerical flux on the large template obtained in step 2 Numerical flux on a small template and the corresponding target cell boundary The linear weight d of each small template is obtained by the method of undetermined coefficients m ; Step 4: Reconstruct the viscosity numerical flux function p of each small template based on step 2 m (x) Obtain the corresponding smoothing factor on the small template; Step 5: Based on the linear weights d of each small template in step 3 m and the smoothing factor β from step 4 m , obtain the nonlinear weight ω on each small template m ; Step 6: Based on the nonlinear weights on each small template and the target unit boundaries on each small template Viscous numerical flux on Get the final target cell boundary Viscous numerical flux on ; Step 7: Repeat steps 2-6 to obtain the final target cell boundary Viscous numerical flux on Step 8: Use the WENO difference scheme to discretize the inviscid numerical flux corresponding to the final viscous numerical flux on the target unit boundary obtained in steps 6 and 7. The time derivatives of the conserved variables in the flow field are obtained by using the conservative semi-discrete format of the governing equations. The derivative of the conserved variable with respect to time in the convection field The variable values ​​in the flow field are obtained by advancing the solution in time.

2. The flow field analysis method of supersonic viscous fluid according to claim 1, characterized in that: The object of flow field analysis is a supersonic aircraft.

3. The flow field analysis method of supersonic viscous fluid according to claim 2, characterized in that: The initial and boundary conditions are supersonic far-field incoming flow conditions.

4. The flow field analysis method of supersonic viscous fluid according to claim 1, characterized in that: The reconstruction-based integral function is used to obtain the reconstructed viscosity numerical flux function p(x) on the large template, which is expressed as: Among them, x represents the input parameter; x j represents the jth grid unit; G(u(x j ),u x (x j )) represents the viscosity term of the governing equation in the grid cell x in the corresponding template j Function value on u(x j ) represents the jth grid cell x j The function value of the independent variable on u x (x j ) represents the jth grid cell x j The derivative of the function of the independent variable on .

5. The flow field analysis method of supersonic viscous fluid according to claim 4, characterized in that: Based on the viscous numerical flux function p(x) obtained in the above steps, the target unit boundary on the large template is obtained Viscous numerical flux on The expression is:

6. The flow field analysis method of supersonic viscous fluid according to claim 1, characterized in that: The reconstruction viscosity numerical flux function p of each small template is obtained by using the reconstruction-based integral function m (x), the expression is: Among them, x represents the input parameter; x j represents the jth grid unit; G(u(x j ),u x (x j )) represents the viscosity term of the governing equation in the grid cell x in the corresponding template j Function value on u(x j ) represents the jth grid cell x j The function value of the independent variable on u x (x j ) represents the jth grid cell x j The derivative of the function of the independent variable on .

7. The flow field analysis method of supersonic viscous fluid according to claim 1, characterized in that: In step 3, the linear weight d of each small template m The expression is: Among them, d m represents the linear weight of the mth small template; Indicates that the large template S calculated in step 2 is at the boundary of the target unit The corresponding viscous numerical flux; Represents the small template S obtained by step 2 m In the target unit The corresponding viscous numerical flux.

8. The flow field analysis method of supersonic viscous fluid according to claim 1, characterized in that: In step 4, the expression of the smoothing factor is: Among them, β m represents the smoothing factor of the mth small template; r represents the number of grid cells on the small template; xJ represents the coordinates of the center point of the Jth target unit discrete point; xJ+1 represents the coordinates of the center point of the J+1th target unit discrete point; It represents the l-th derivative of the flux function along the x-axis, where l = 1, 2, …, r; dx represents the integration of the x-th input parameter.

9. The flow field analysis method of supersonic viscous fluid according to claim 8, characterized in that: Nonlinear weight ω on small template m , the expression is: Among them, ω m Represents the nonlinear weight on the mth small template; Represents the nonlinear weight of the intermediate process; d m represents the linear weight of the mth small template; ε represents a small positive number to avoid the denominator being 0.

10. The flow field analysis method of supersonic viscous fluid according to any one of claims 1 to 9, characterized in that: The variable values ​​in the flow field obtained in step 8 are density, momentum in the x-axis direction, momentum in the y-axis direction, and total energy.

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