A compact finite central difference flow field analysis method based on reconstruction

Abstract

The present invention relates to a reconstruction-based compact finite center difference flow field analysis method, which belongs to the technical field of fluid mechanics numerical calculation. The present invention first uses a reconstruction-based method to numerically discretize the outer derivative of the viscosity term in the Navier-Stokes equations for fluid aerodynamic control, thereby obtaining a viscous numerical flux defined at the unit center. For the inner derivative at the unit center, a Lagrangian interpolation function is constructed and its derivative function is obtained to perform a discrete solution, thereby obtaining an interpolation expression at the corresponding point. Finally, the discretization work of the finite difference format is completed, and the Navier-Stokes equations for fluid aerodynamic control are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid mechanics numerical calculation, and in particular to a flow field analysis method based on reconstructed compact finite central difference, and in particular to a solution method for the Navier-Stokes equations used in flow field analysis based on reconstructed compact finite central difference. Background Art

[0002] Based on the continuum assumption, the Navier-Stokes equations are one of the key governing equations in aerodynamics. They extensively describe the flow states of various fluids in nature, including both compressible and incompressible fluids. They hold significant research significance and application value in fields such as complex flow calculations for aircraft, turbulence mechanism research, aerodynamic optimization design, and ship protection simulation. However, the existence and uniqueness of solutions to these governing equations remain elusive, leading to their numerical solution. By setting different initial and boundary conditions in the flow field and advancing the equation to a steady state or a given computational time through explicit or implicit time progression, the flow characteristics of the flow field in the computational domain can be effectively captured, allowing for a better understanding of the flow mechanisms within the flow field. This, in turn, allows for solutions to practical problems such as aircraft design optimization.

[0003] As a traditional high-precision numerical calculation method, the finite difference method is widely used to solve the Navier-Stokes equations under various conditions due to its advantages such as high accuracy, high efficiency, low storage requirements, easy programming, and comprehensive theoretical knowledge. Because the inviscid and viscous terms in the governing equations represent different physical properties, numerically solving the governing equations using the finite difference method requires discretizing these two terms separately, thus completing the spatial discretization. Finally, the final numerical solution is achieved through time advancement, ultimately obtaining the physical characteristics of the flow field, such as density, velocity, and pressure, through calculation.

[0004] In the existing technology, there are many problems with the finite difference method commonly used in flow field analysis. In the finite difference method, in order to capture discontinuous features such as shock waves that may appear in flow field calculations, people have developed a series of numerical discretization formats for inviscid terms, such as ENO, WENO, TENO, WCNS, etc. These numerical discretization formats play a very important role in suppressing non-physical oscillations of the flow field. However, in the discretization of viscous terms, people usually use the traditional central difference format. The traditional central difference format first performs central interpolation on the outer derivative of the viscosity term, and then uses the same central interpolation method to numerically discretize the inner derivative at the interpolation point. This discretization method requires a large number of numerical template points. The traditional central difference format with 2r-order format accuracy requires (4r+1) template units to complete the discretization of this unit. This discretization format will cause a series of disadvantages: (1) A large number of template units makes the boundary processing of the problem more complicated; (2) A large number of template units increases the amount of calculation in each viscous flux calculation process; (3) The number of template units for the viscosity term far exceeds the number of template units for the non-viscous term, making it impossible to fully and effectively use the information in the flow field. Summary of the Invention

[0005] In view of the above problems, the present invention provides a reconstruction-based compact finite center difference flow field analysis method. The present invention first uses a reconstruction-based method to numerically discretize the outer derivative of the viscosity term in the Navier-Stokes equations of fluid aerodynamic control, thereby obtaining a viscous numerical flux defined at the unit center. For the inner derivative at the unit center, a Lagrangian interpolation function is constructed and its derivative function is obtained for discrete solution, thereby obtaining the interpolation expression at the corresponding point, and finally completing the discretization work of the finite difference format to solve the Navier-Stokes equations of fluid aerodynamic control.

[0006] The present invention provides a reconstruction-based compact finite central difference flow field analysis method, comprising:

[0007] Step S1, obtaining initial conditions, boundary conditions, the fluid aerodynamic control Navier-Stokes equations to be solved in the flow field analysis, and the region to be analyzed;

[0008] The initial conditions include density, velocity and / or pressure;

[0009] The boundary conditions include free flow and / or reflection boundary conditions;

[0010] The area to be analyzed is divided into a structured grid to obtain a plurality of grid units; each of the grid units includes a left boundary and a right boundary; wherein the jth grid unit includes a left boundary of and the right boundary is

[0011] Step S2, let t = 0, when t = 0 is the initial time;

[0012] Step S3: Determine the target grid cell x at time t in the area to be analyzed J,t ; Take the target grid cell x J,t As the center, 2r grid units are symmetrically selected to form a large template S, and reconstruction is performed on the large template S as the template unit S at time t, t={x J-r,t ,...,x J+r-1,t};

[0013] Step S4: perform implicit definition on the template unit at time t to obtain the implicit definition function at time t;

[0014] Preferably, the expression of the implicitly defined function at time t is:

[0015]

[0016] Where Δx,t is the size of the grid cell at time t along the x direction; p(x,t) is the viscosity flux reconstructed within the cell at time t along the x direction; G = G(u,u x,t ) is the viscosity term in the x-direction of the Navier-Stokes equations governing fluid aerodynamics to be solved in flow field analysis, u x,t is the partial derivative function value along the x direction; G(x j,t ) is the viscosity term of the fluid aerodynamic control Navier-Stokes equation along the x-axis direction in the flow field analysis at the coordinate position x j The value of the corresponding sticky term is j = {Jr,…,J+r-1}.

[0017] Step S5: Obtain the number of units 2r in the template unit at time t; define a (2r-1)-order polynomial based on the number of units 2r in the template unit at time t, expressed as:

[0018]

[0019] Among them, a k is the kth unknown coefficient to be determined; x k is the k-th derivative along the x direction.

[0020] Step S6: Substitute the (2r-1) degree polynomial into the implicit definition function at the time t to obtain an updated (2r-1) degree polynomial;

[0021] Step S7: Based on the updated (2r-1) times polynomial, the right edge of the template unit at time t is obtained. The numerical flux equation of fluid viscosity on is expressed as:

[0022]

[0023] in, is the right edge of the template unit at time t along the x direction The numerical flux of fluid viscosity on , is the right boundary of the cell reconstructed at time t along the x direction The viscosity numerical flux.

[0024] Step S8, perform Lagrange interpolation on the center of the template unit at time t on the same large template S and obtain the derivative function, and obtain the inner derivative function value of the template unit center in the flow field at time t; the inner derivative function value includes: the partial derivative function value u along the x-axis direction x,t and the partial derivative function value u along the y-axis y,t ;

[0025] Step S9: Substitute the inner derivative function value of the template unit center in the flow field at time t in step S8 into the fluid viscosity numerical flux equation on the right boundary of the template unit at time t in step S7 to obtain the viscosity numerical flux of the template unit at time t with a 2r-order format accuracy.

[0026] Replace the right boundary of the template unit at time t with the left boundary, and let Repeat steps S7-S9 to obtain the viscosity numerical flux of 2r order format accuracy on the left boundary of the template unit at time t

[0027] The viscosity numerical flux of the fluid along the x direction at time t is obtained based on the viscosity numerical flux of the 2r-order format accuracy on the left boundary of the template unit at time t and the viscosity numerical flux of the 2r-order format accuracy on the right boundary of the template unit at time t;

[0028] Step S10: Replace the x direction in step S3 with the y direction, and repeat steps S3-S9 to obtain the viscous numerical flux of the fluid along the y direction at time t;

[0029] The viscosity numerical flux of the fluid at time t is obtained based on the viscosity numerical flux of the fluid along the x direction at time t and the viscosity numerical flux of the fluid along the y direction at time t;

[0030] Step S11: Obtain the inviscid term F1 and the inviscid term F2 in the fluid aerodynamics control equation to be solved at time t, discretize the inviscid term F1 and the inviscid term F2 using the weighted essential non-oscillation method, and obtain the fluid inviscid numerical flux at time t. and the fluid inviscid numerical flux at time t

[0031] The inviscid numerical flux of the fluid at time t is and the fluid inviscid numerical flux at time t Get the inviscid numerical flux of the fluid at time t;

[0032] Step S12: rewrite the viscous numerical flux of the fluid at time t and the inviscid numerical flux of the fluid at time t into a conservative semi-discrete format to obtain the rewritten Navier-Stokes equations governing fluid aerodynamics, which are expressed as follows:

[0033]

[0034] Where u is the velocity component in the x direction and is a conserved variable, is the numerical flux of the inviscid right boundary of the fluid at time t, is the numerical flux of the left boundary of the fluid inviscid term at time t, is the viscous numerical flux of 2r-order format accuracy on the right boundary of the template element at time t, is the viscous numerical flux of the fluid along the y direction at time t; Δy,t is the size of the grid unit along the y direction at time t.

[0035] Update the conserved variables in the semi-discrete equation of the conservation form of the rewritten Navier-Stokes equation; solve it using the third-order Runge-Kutta method to obtain an approximate solution at time t;

[0036] The approximate solution at time t includes the density of the fluid at time t, the velocity component in the x direction at time t, the velocity component in the ty direction at time t, the pressure at time t and / or the total energy at time t;

[0037] Step S13: Determine whether t is greater than or equal to T, where T represents the total time. If so, take the approximate solution at time t as the final approximate solution and output it to obtain the flow field analysis result; if not, set t=t+1 and return to step S2.

[0038] Preferably, the fluid aerodynamic control Navier-Stokes equation to be solved in step S1 is expressed as:

[0039]

[0040] Among them, U is the conserved variable to be solved, F1 is the first inviscid term, F2 is the second inviscid term, G1 is the first viscous term, and G2 is the second viscous term;

[0041]

[0042] Where ρ is the density, u is the velocity component in the x direction, v is the velocity component in the y direction, p is the pressure, E is the total energy, τ is the stress variable, q is the heat flux, τ xy is the stress acting on the x-plane in the y-direction, τ xx is the normal stress along the x direction; τ yy is the normal stress along the y direction.

[0043] Furthermore, the expressions of the stress variable and heat flux are:

[0044]

[0045] Where ρ is the density, u is the velocity component in the x direction, v is the velocity component in the y direction, T is the temperature of the fluid, Pr is the corresponding Prandtl constant, γ is the heat flow constant, which is 1.4 for ideal gas; τ xy is the stress acting on the x-plane in the y-direction, τ xx is the normal stress along the x direction; τ yy is the normal stress along the y direction, μ is the viscosity coefficient, q x is the heat flux in the x direction, q y is the heat flux in the y direction.

[0046] Compared with the prior art, the present invention has at least the following beneficial effects:

[0047] (1) The present invention processes the external derivative in the viscosity term by reconstruction, so that the viscosity numerical flux is defined at the unit center point. The function value at the unit center point can be directly obtained through the flow field information without the need for interpolation calculation again, thereby reducing the amount of calculation;

[0048] (2) The present invention calculates the numerical flux defined at the cell center by directly using Lagrang interpolation based on the reconstructed template cell and taking its derivative function, thereby effectively reducing the number of template cells while achieving format accuracy and simplifying the form of the expression;

[0049] (3) Compared with the traditional central difference format which requires (4r+1) template units, the 2r-order central difference format of the present invention only requires (2r+1) template units, thereby effectively reducing the number of template units required in the discretization process of the viscosity term;

[0050] (4) The 2r-order central difference format of the present invention only requires r virtual grid cells on the boundary, which is consistent with the number of template cells required for the (2r-1)-order format without sticky terms. Therefore, based on the same number of template cells, the (2r-1)-order format accuracy can be achieved overall, making full use of the function information of the template cells.

[0051] (5) Since the number of template units required on the boundary is relatively small, the method reduces the requirements for boundary processing and improves the practical application scenarios of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The drawings are only for purposes of illustrating particular embodiments and are not to be considered limiting of the invention.

[0053] Figure 1 Schematic diagram of a discrete grid in one dimension according to an embodiment of the present invention;

[0054] Figure 2 Schematic diagram of a grid decomposition diagram of a two-dimensional viscous shock tube calculation area in an embodiment of the present invention;

[0055] Figure 3 Schematic diagram of the flow field initialization state density map at time t=0.0 in an embodiment of the present invention;

[0056] Figure 4 Schematic diagram of the calculated flow field density map when t=1.0 in an embodiment of the present invention. DETAILED DESCRIPTION

[0057] 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.

[0058] A specific embodiment of the present invention, as Figure 1-4 , discloses a compact finite central difference flow field analysis method based on reconstruction. To illustrate the effectiveness of the method proposed in the present invention, the technical solution of the present invention is described in detail below using a specific sixth-order accuracy (r=3) central difference as an example. The specific implementation steps are as follows:

[0059] Step S1, obtaining initial conditions, boundary conditions, the fluid aerodynamic control Navier-Stokes equations to be solved in the flow field analysis, and the region to be analyzed;

[0060] The initial conditions include density, velocity and / or pressure;

[0061] The boundary conditions include free flow and / or reflection boundary conditions;

[0062] The area to be analyzed is divided into a structured grid to obtain a plurality of grid units; each of the grid units includes a left boundary and a right boundary; wherein the jth grid unit includes a left boundary of and the right boundary is

[0063] Step S2, let t = 0, when t = 0 is the initial time;

[0064] Step S3: Determine the target grid cell x at time t in the area to be analyzed J,t ; Take the target grid cell x J,t As the center, 2r grid units are symmetrically selected to form a large template S, and reconstruction is performed on the large template S as the template unit S at time t, t={x J-r,t ,...,x J+r-1,t};

[0065] Step S4: perform implicit definition on the template unit at time t to obtain the implicit definition function at time t;

[0066] Preferably, the expression of the implicitly defined function at time t is:

[0067]

[0068] Where Δx,t is the size of the grid cell at time t along the x direction; p(x,t) is the viscosity flux reconstructed within the cell at time t along the x direction; G = G(u,u x,t ) is the viscosity term in the x-direction of the Navier-Stokes equations governing fluid aerodynamics to be solved in flow field analysis, u x,t is the partial derivative function value along the x direction; G(x j,t ) is the viscosity term of the fluid aerodynamic control Navier-Stokes equation along the x-axis direction in the flow field analysis at the coordinate position x j The value of the corresponding sticky term is j = {Jr,…,J+r-1}.

[0069] Step S5: Obtain the number of units 2r in the template unit at time t; define a (2r-1)-order polynomial based on the number of units 2r in the template unit at time t, expressed as:

[0070]

[0071] Among them, a k is the kth unknown coefficient to be determined; x k is the k-th derivative along the x direction.

[0072] Step S6: Substitute the (2r-1) degree polynomial into the implicit definition function at the time t to obtain an updated (2r-1) degree polynomial;

[0073] Step S7: Based on the updated (2r-1) times polynomial, the right edge of the template unit at time t is obtained. The numerical flux equation of fluid viscosity on is expressed as:

[0074]

[0075] in, is the right edge of the template unit at time t along the x direction The numerical flux of fluid viscosity on , is the right boundary of the cell reconstructed at time t along the x direction The viscosity numerical flux.

[0076] Step S8, perform Lagrange interpolation on the center of the template unit at time t on the same large template S and obtain the derivative function, and obtain the inner derivative function value of the template unit center in the flow field at time t; the inner derivative function value includes: the partial derivative function value u along the x-axis direction x,t and the partial derivative function value u along the y-axis y,t ;

[0077] Step S9: Substitute the inner derivative function value of the template unit center in the flow field at time t in step S8 into the fluid viscosity numerical flux equation on the right boundary of the template unit at time t in step S7 to obtain the viscosity numerical flux of the template unit at time t with a 2r-order format accuracy.

[0078] Replace the right boundary of the template unit at time t with the left boundary, and let Repeat steps S7-S9 to obtain the viscosity numerical flux of 2r order format accuracy on the left boundary of the template unit at time t

[0079] The viscosity numerical flux of the fluid along the x direction at time t is obtained based on the viscosity numerical flux of the 2r-order format accuracy on the left boundary of the template unit at time t and the viscosity numerical flux of the 2r-order format accuracy on the right boundary of the template unit at time t;

[0080] Step S10: Replace the x direction in step S3 with the y direction, and repeat steps S3-S9 to obtain the viscous numerical flux of the fluid along the y direction at time t;

[0081] The viscosity numerical flux of the fluid at time t is obtained based on the viscosity numerical flux of the fluid along the x direction at time t and the viscosity numerical flux of the fluid along the y direction at time t;

[0082] Step S11: Obtain the inviscid term F1 and the inviscid term F2 in the fluid aerodynamics control equation to be solved at time t, discretize the inviscid term F1 and the inviscid term F2 using the weighted essential non-oscillation method, and obtain the fluid inviscid numerical flux at time t. and the fluid inviscid numerical flux at time t

[0083] The inviscid numerical flux of the fluid at time t is and the fluid inviscid numerical flux at time t Get the inviscid numerical flux of the fluid at time t;

[0084] Step S12: rewrite the viscous numerical flux of the fluid at time t and the inviscid numerical flux of the fluid at time t into a conservative semi-discrete format to obtain the rewritten Navier-Stokes equations governing fluid aerodynamics, which are expressed as follows:

[0085]

[0086] Where u is the velocity component in the x direction and is a conserved variable, is the numerical flux of the inviscid right boundary of the fluid at time t, is the numerical flux of the left boundary of the fluid inviscid term at time t, is the viscous numerical flux of 2r-order format accuracy on the right boundary of the template element at time t, is the viscous numerical flux of the fluid along the y direction at time t; Δy,t is the size of the grid unit along the y direction at time t.

[0087] Update the conserved variables in the semi-discrete equation of the conservation form of the rewritten Navier-Stokes equation; solve it using the third-order Runge-Kutta method to obtain an approximate solution at time t;

[0088] The approximate solution at time t includes the density of the fluid at time t, the velocity component in the x direction at time t, the velocity component in the ty direction at time t, the pressure at time t and / or the total energy at time t;

[0089] Step S13: Determine whether t is greater than or equal to T, where T represents the total time. If so, take the approximate solution at time t as the final approximate solution and output it to obtain the flow field analysis result; if not, set t=t+1 and return to step S2.

[0090] Preferably, the fluid aerodynamic control Navier-Stokes equation to be solved in step S1 is expressed as:

[0091]

[0092] Among them, U is the conserved variable to be solved, F1 is the first inviscid term, F2 is the second inviscid term, G1 is the first viscous term, and G2 is the second viscous term;

[0093]

[0094] Where ρ is the density, u is the velocity component in the x direction, v is the velocity component in the y direction, p is the pressure, E is the total energy, τ is the stress variable, q is the heat flux, τ xy is the stress acting on the x-plane in the y-direction, τ xx is the normal stress along the x direction; τ yy is the normal stress along the y direction.

[0095] Furthermore, the expressions of the stress variable and heat flux are:

[0096]

[0097] Where ρ is the density, u is the velocity component in the x direction, v is the velocity component in the y direction, T is the temperature of the fluid, Pr is the corresponding Prandtl constant, γ is the heat flow constant, which is 1.4 for ideal gas; τ xy is the stress acting on the x-plane in the y-direction, τ xx is the normal stress along the x direction; τ yy is the normal stress along the y direction, μ is the viscosity coefficient, q x is the heat flux in the x direction, q y is the heat flux in the y direction.

[0098] 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 compact finite central difference flow field analysis method based on reconstruction, characterized in that: include: Step S1, obtaining initial conditions, boundary conditions, the fluid aerodynamic control Navier-Stokes equations to be solved in the flow field analysis, and the region to be analyzed; performing structured grid division on the region to be analyzed to obtain a plurality of grid cells; each of the grid cells includes a left boundary and a right boundary; Step S2, let t = 0, when t = 0 is the initial time; Step S3: determining the target grid cell at time t in the area to be analyzed; With the target grid cell as the center, 2r grid cells are symmetrically selected for reconstruction as the template cell at time t; Step S4: perform implicit definition on the template unit at time t to obtain the implicit definition function at time t; Step S5, obtaining the number of units 2r in the template unit at time t; defining a (2r-1)-order polynomial according to the number of units 2r in the template unit at time t; Step S6: Substitute the (2r-1) degree polynomial into the implicit definition function at the time t to obtain an updated (2r-1) degree polynomial; Step S7: Based on the updated (2r-1)-order polynomial, obtain the fluid viscosity numerical flux equation on the right boundary of the template unit at time t; Step S8, performing Lagrange interpolation on the center of the template unit at time t and obtaining the derivative function, respectively obtaining the inner derivative function value of the center of the template unit at time t in the flow field; Step S9, substituting the inner derivative function value of the template unit center in the flow field at time t in step S8 into the fluid viscosity numerical flux equation on the right boundary of the template unit at time t in step S7, to obtain the viscosity numerical flux on the right boundary of the template unit at time t with a 2r-order format accuracy; Replace the right boundary of the template unit at time t with the left boundary, repeat steps S7-S9, and obtain the viscous numerical flux of the 2r-order format accuracy on the left boundary of the template unit at time t; Based on the viscous numerical flux of the 2r-order format accuracy on the left boundary of the template unit at time t and the viscous numerical flux of the 2r-order format accuracy on the right boundary of the template unit at time t, the viscous numerical flux of the fluid along the x direction at time t is obtained; Step S10: Replace the x direction in step S3 with the y direction, and repeat steps S3-S9 to obtain the viscous numerical flux of the fluid along the y direction at time t; The viscosity numerical flux of the fluid at time t is obtained based on the viscosity numerical flux of the fluid along the x direction at time t and the viscosity numerical flux of the fluid along the y direction at time t; Step S11: obtaining an inviscid term in the fluid aerodynamics control equation to be solved at time t, discretizing the inviscid term using a weighted essential inoscillation method to obtain an inviscid numerical flux of the fluid at time t; obtaining an inviscid numerical flux of the fluid at time t based on the inviscid numerical flux of the fluid at time t; Step S12: rewrite the viscous numerical flux of the fluid at time t and the inviscid numerical flux of the fluid at time t into a conservative semi-discrete format to obtain the rewritten Navier-Stokes equations governing fluid aerodynamics; Update the conserved variables in the rewritten Navier-Stokes equations for fluid aerodynamics control; solve them using the third-order Runge-Kutta method to obtain an approximate solution at time t; Step S13: Determine whether t is greater than or equal to T, where T represents the total time. If so, take the approximate solution at time t as the final approximate solution and output it; if not, set t=t+1 and return to step S2.

2. The reconstruction-based compact finite central difference flow field analysis method according to claim 1, characterized in that: The initial conditions in step S1 include density, velocity and / or pressure; The boundary conditions include free-flow and / or reflecting boundary conditions.

3. The reconstruction-based compact finite central difference flow field analysis method according to claim 1, characterized in that: The fluid aerodynamic control Navier-Stokes equation to be solved in step S1 is expressed as follows: Among them, U is the conserved variable to be solved, F1 is the first inviscid term, F2 is the second inviscid term, G1 is the first viscous term, and G2 is the second viscous term.

4. The reconstruction-based compact finite central difference flow field analysis method according to claim 1, characterized in that: The expression of the implicitly defined function at time t in step S4 is: Where Δx,t is the size of the grid cell at time t along the x direction; p(x,t) is the viscosity flux reconstructed in the cell at time t along the x direction; G(x j,t ) is the viscosity term of the fluid aerodynamic control Navier-Stokes equation along the x direction at the coordinate position x in the flow field analysis. j The value of the corresponding sticky item, is the left boundary of the j-th grid cell, is the right boundary of the j-th grid cell.

5. The reconstruction-based compact finite central difference flow field analysis method according to claim 1, characterized in that: Right edge of template unit at time t The numerical flux equation of fluid viscosity on is expressed as: in, The right edge of the template unit at time t along the x-axis The numerical flux of fluid viscosity on , The right boundary of the cell reconstructed at time t along the x-axis direction The viscosity numerical flux.

6. The reconstruction-based compact finite central difference flow field analysis method according to claim 1, characterized in that: The inner derivative function value includes: a partial derivative function value along the x-axis direction and a partial derivative function value along the y-axis direction.

7. The reconstruction-based compact finite central difference flow field analysis method according to claim 1, characterized in that: The rewritten Navier-Stokes equations governing fluid aerodynamics are expressed as follows: Among them, u is the velocity component in the x direction, which is a conserved variable. is the numerical flux of the inviscid right boundary of the fluid at time t, is the numerical flux of the left boundary of the fluid inviscid term at time t, is the viscous numerical flux of 2r-order format accuracy on the right boundary of the template element at time t, is the viscous numerical flux of the fluid along the y direction at time t; Δy,t is the size of the grid unit along the y direction at time t.

8. The reconstruction-based compact finite central difference flow field analysis method according to claim 1, characterized in that: The specific steps of obtaining the inviscid numerical flux of the fluid at time t in step S11 include: Step S11, obtaining an inviscid term 1 and an inviscid term 2 in the fluid aerodynamics control equation to be solved at time t, discretizing the inviscid term 1 and the inviscid term 2 using a weighted essential inoscillation method, and obtaining an inviscid numerical flux 1 of the fluid at time t and an inviscid numerical flux 2 of the fluid at time t; The fluid inviscid numerical flux at time t is obtained based on the fluid inviscid numerical flux one at time t and the fluid inviscid numerical flux two at time t.

9. The reconstruction-based compact finite central difference flow field analysis method according to claim 1, characterized in that: Step S13: The approximate solution at time t includes the density of the fluid at time t, the velocity component in the x direction at time t, the velocity component in the y direction at time t, the pressure at time t and / or the total energy at time t.

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