Stability analysis method of two-dimensional gas kinetic flow based on finite difference scheme

Abstract

This invention discloses a two-dimensional gas kinetic flow stability analysis method based on a finite difference scheme, relating to the field of aerodynamics research. The method includes: selecting the BGK model as the initial model; introducing a reduced distribution function to obtain a model about the reduced distribution function; obtaining the small perturbation equation; obtaining the relationship between the reduced distribution function of the perturbation and the macroscopic quantity of the perturbation; obtaining the stability equation; deriving the diffuse boundary conditions corresponding to the perturbation; obtaining the objective equation and objective boundary conditions; solving for eigenvalues ​​and eigenvectors based on the objective equation, the objective boundary conditions, and given parameters; and obtaining the analysis results of the two-dimensional gas kinetic flow stability analysis based on the eigenvalue and eigenvector solution results. The coefficient matrix obtained by discretizing using the finite difference scheme in this method is sparser, reducing matrix storage and computational complexity.

Description

Technical Field

[0001] The invention relates to the field of aerodynamic research, and in particular to a two-dimensional gas kinetic flow stability analysis method based on a finite difference format. Background Art

[0002] For near-space hypersonic vehicles, the boundary layer transition causes the friction and heat flow on their surface to increase by 3 to 5 times, seriously affecting flight performance and safety. In large airspace flight environments, the influence of rarefied gas effects cannot be ignored, and traditional analysis theories and methods based on the Navier-Stokes equations are no longer applicable. The existing rarefied flow stability analysis method developed based on the Boltzmann equation provides a new means for transition height prediction. However, this method uses the Chebyshev spectrum method, and all points in the flow field space need to be selected for discretization. The generated matrix is ​​relatively dense, which places a great test on the demand for computing resources. Summary of the invention

[0003] In order to overcome the shortcomings of the prior art, the present invention provides a two-dimensional gas kinetic flow stability analysis method based on the finite difference format. The coefficient matrix obtained by discretizing the finite difference format is more sparse, which reduces the matrix storage and calculation amount, thereby solving the problem of long calculation time when there are many physical space points and velocity space points in the prior art.

[0004] To achieve the above-mentioned object of the invention, the present invention provides a two-dimensional gas kinetic flow stability analysis method based on a finite difference format, the method comprising:

[0005] Step 1: Select the BGK model as the initial model;

[0006] Step 2: introducing a reduced distribution function, eliminating the dependence of the distribution function on the molecular velocity in the vertical direction in the initial model, and obtaining a model of the reduced distribution function;

[0007] Step 3: Under the condition that the rarefied gas satisfies the parallelism hypothesis and the small perturbation hypothesis, the instantaneous quantity in the model about the reduced distribution function is rewritten into the form of the sum of the basic flow and the perturbation quantity; under the condition that the basic flow satisfies the model about the reduced distribution function, the small perturbation equation is obtained;

[0008] Step 4: Process the perturbation reduced distribution function in the small perturbation equation by moment calculation to obtain the relationship between the perturbation reduced distribution function and the perturbation macroscopic quantity;

[0009] Step 5: Write the disturbance in the small disturbance equation as the product of the shape function and the wave function to obtain the stability equation;

[0010] Step 6: Using diffuse reflection boundary conditions, derive the diffuse reflection boundary conditions corresponding to the disturbance under the assumption of small disturbance;

[0011] Step 7: Based on the relationship between the disturbance reduced distribution function and the disturbance macroscopic quantity, the stability equation and the boundary conditions of the disturbance are discretized to obtain the target equation and target boundary conditions;

[0012] Step 8: Solve the eigenvalues ​​and eigenvectors based on the target equation, the target boundary conditions and given parameters, and obtain the analysis results of the two-dimensional gas kinetic flow stability analysis based on the solution results of the eigenvalues ​​and eigenvectors.

[0013] The present invention proposes a rarefied flow stability analysis method based on a finite difference format. As a local method, the finite difference format can reduce the proportion of non-zero elements in the matrix during discretization, thereby improving computational efficiency and storage space requirements.

[0014] Among them, step 7 of the present invention uses a specified method to discretize the stability equation and the boundary conditions of the disturbance to obtain the target equation and the target boundary conditions; wherein the specified method includes a finite difference format and a Gauss-Hermite velocity space discretization method.

[0015] The present invention adopts the implicit restart Arnoldi algorithm to solve the eigenvalue problem; the calculated eigenvalue results are compared with the spectral method results in terms of calculation accuracy and efficiency, and the superiority of the finite difference format is analyzed.

[0016] Among them, the two-dimensional BGK initial model is:

[0017] ;

[0018] in, f = f ( t , x , y , ξ x , ξ y , ξ z ) represents the distribution function of particles with respect to time, physical space and velocity space, x Indicates the flow direction, y represents the normal direction, ξ x , ξ y and ξ z are the particle velocities in the streamwise, normal and spanwise directions, respectively. t Indicates time, a x represents the acceleration in the flow direction, T Indicates temperature, ρ is the density, f e The particle equilibrium distribution function, K is the Knudsen number, μ Indicates viscosity.

[0019] Among them, the reduced distribution function is:

[0020] ;

[0021] in: g ( t , x , y , ξ x , ξ y )= g is the reduced distribution function;

[0022] The reduced distribution function is introduced into the model equation:

[0023] ;

[0024] in: g e represents the particle reduced equilibrium distribution function;

[0025] ;

[0026] in, ξ =( ξ x , ξ y ) represents the particle velocity, u =( u , v ) represents the macroscopic speed, u is the flow velocity, v is the normal velocity, R represents the particle equilibrium constant.

[0027] Among them, this method uses the distribution function to find the moment to determine the relationship between the reduced distribution function and the macroscopic quantity. The expressions of density and macroscopic velocity are as follows:

[0028] ;

[0029] ;

[0030] Among them, under the condition that the rarefied gas satisfies the parallelism assumption and the small disturbance assumption, the instantaneous quantity in the model of the reduced distribution function is rewritten as the sum of the basic flow and the disturbance quantity, specifically including:

[0031] ;

[0032] in, t Indicates time, x Indicates the flow direction, y represents the normal direction, ξ x and ξ y are the particle velocities in the streamwise and normal directions, respectively, u is the flow velocity, v is the normal velocity, for g The basic amount, for g The disturbance amount, g e represents the particle reduced equilibrium distribution function, for g e The basic amount, for g e The disturbance amount, ρ is the density, for ρ The basic amount, for ρ The disturbance amount, for u The basic amount, for u The disturbance amount, v The basic amount is 0, for v The amount of disturbance;

[0033] The small perturbation equation is initially constructed as:

[0034] ;

[0035] Eliminating the basic flow term and nonlinear term, the small perturbation equation is obtained:

[0036] ;

[0037] in, a x represents the acceleration in the flow direction, K is the Knudsen number, R represents the particle equilibrium constant.

[0038] The perturbation quantity in the small perturbation equation is written as the product of the shape function and the wave function, specifically:

[0039] ;

[0040] in, e is the natural base, i is an imaginary number, a is the wave number, is the frequency, for ρ The amplitude of for g The amplitude of for u The amplitude of for v The amplitude of for g e The amplitude of

[0041] The stability equation is:

[0042] .

[0043] Among them, the perturbation reduced distribution function in the small perturbation equation is processed by moment calculation to obtain the relationship between the perturbation reduced distribution function and the perturbation macroscopic quantity, specifically:

[0044] ;in, ξ Represents the particle speed.

[0045] Among them, the diffuse reflection boundary condition corresponding to the disturbance is:

[0046] ;

[0047] in: represents the reduced perturbation distribution function on the particle boundary, r w represents the position on the particle boundary, h Indicates the time interval, represents the equilibrium perturbation distribution function on the particle boundary, ρ w represents the boundary perturbation density, u w represents the average velocity of the streamwise disturbance on the boundary, n represents the normal vector of the boundary, t Indicates time, ξ represents the particle velocity;

[0048] ρ w It is expressed as:

[0049] ;

[0050] in, represents the equilibrium perturbation distribution function on the particle boundary;

[0051] It is expressed as:

[0052] ;

[0053] in, R represents the particle equilibrium constant, ξ x and ξ y are the particle velocities in the streamwise and normal directions, respectively.

[0054] In an optional embodiment of the present specification, the target stability equation is discretized using the finite difference method and the Gauss-Hermite velocity space discretization method. The discretization form of the stability equation is:

[0055] ;

[0056] in, N Indicates the number of physical space points, j Indicates the current point in physical space. represents the finite difference scheme coefficients, i is an imaginary number, a is the wave number, K is the Knudsen number, for ρ The basic amount, In velocity space, k The normal discrete particle velocity, Represents a point in physical space p Speed ​​Space Point k The reduced perturbation distribution function of In velocity space, k The particle velocity of the stream, Represents a point in physical space j Speed ​​Space Point k The reduced perturbation distribution function of Represents a point in physical space j Speed ​​Space Point k The basic quantity of the equilibrium distribution function, Represents a point in physical space j Speed ​​Space Point k The basic quantity of the reduced distribution function, W l represents the weight coefficient, Q represents a velocity space point, Represents a point in physical space j Speed ​​Space Point l The reduced perturbation distribution function of Represents a point in physical space j Flow to macro velocity, Represents a velocity space point l The particle velocity of the stream, Represents a velocity space point l The normal particle velocity;

[0057] The discrete form corresponding to the perturbed boundary condition is:

[0058] ;

[0059] in, represents the velocity space point on the boundary k Reduced perturbation distribution function, represents the velocity space point on the boundary k The basic quantity of the reduced perturbation equilibrium distribution function, The basic quantity representing the distribution function of the reduced perturbation equilibrium state that satisfies the molecular velocity condition on the boundary, W up is the upper surface integral weight coefficient, W low is the integral weight coefficient of the lower surface, represents the reduced perturbation distribution function on the boundary, represents the boundary point, ρ c is the basic quantity of density, ξ y is the particle velocity in the normal direction.

[0060] In an optional embodiment of the present specification, after step 8, the method further includes:

[0061] Based on the analysis results of two-dimensional gas kinetic flow stability analysis and the shape parameters of the aircraft model, the transition prediction results of the aircraft model are obtained.

[0062] Through this method, the analysis results of two-dimensional gas kinetic flow stability analysis can be obtained efficiently, and then the transition prediction of high-altitude aircraft can be realized efficiently. Compared with the NS equation, by adjusting the Knudsen number, the flow of the entire flow domain from rarefied flow to continuous flow can be described, and the application range is wide. The use of finite difference format can improve the computational efficiency while reducing the memory requirements, making it possible to study the stability problem of strong non-equilibrium flow at higher Mach numbers.

[0063] One or more technical solutions provided by the present invention have at least the following technical effects or advantages:

[0064] The present invention provides a rarefied flow stability analysis method based on a finite difference format. As a local method, the finite difference format can reduce the proportion of non-zero elements in a matrix when discretized, thereby improving computational efficiency and storage space requirements.

[0065] The present application provides a two-dimensional gas kinetic flow stability analysis method based on a finite difference format. The method has the ability to analyze the stability of large Knudsen number and high Mach number flows. Compared with the spectral method, the method is more efficient. The coefficient matrix obtained by discretizing using the finite difference format is sparser, which reduces the matrix storage and calculation amount. It can solve the problem of long calculation time when there are many physical space points and velocity space points in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of the present invention, and do not constitute a limitation on the embodiments of the present invention;

[0067] Figure 1 This is a flow chart of a two-dimensional gas kinetic flow stability analysis method based on a finite difference format in one embodiment of the present application;

[0068] Figure 2 Schematic diagram of comparison of results obtained by a stability analysis method based on a finite difference format and a stability analysis method based on a Chebyshev spectrum method under a continuous flow in an embodiment of the present application, wherein the abscissa is the phase velocity of the modal eigenvalue, and the ordinate is the growth rate of the modal eigenvalue;

[0069] Figure 3 This is a schematic diagram comparing the results obtained by a stability analysis method based on a finite difference format and a stability analysis method based on a Chebyshev spectrum method under rarefied flow in an example of the present application, wherein the horizontal axis is the phase velocity of the modal eigenvalue, and the vertical axis is the growth rate of the modal eigenvalue. DETAILED DESCRIPTION

[0070] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0071] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those within the scope of this description. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0072] Embodiment 1;

[0073] Please refer to Figure 1 The present invention provides a two-dimensional gas kinetic flow stability analysis method based on a finite difference format, specifically comprising:

[0074] S1: Select the BGK model as the initial model.

[0075] In an optional embodiment of this specification, the BGK initial model is:

[0076] ; (1)

[0077] S2: In order to reduce computer storage and improve computing efficiency, a reduced distribution function is introduced:

[0078] ; (2)

[0079] The reduced distribution function is introduced into the model equation:

[0080] ; (3)

[0081] in:

[0082] ; (4)

[0083] S3: Under the condition that the rarefied gas satisfies the parallelism assumption, the instantaneous macroscopic quantity and the reduced distribution function in the reduced distribution function equation are written as the sum of the basic flow and the disturbance quantity, and the disturbance model is simplified, wherein the parallelism assumption means that the flow physical quantity only depends on y in the Cartesian coordinate system and is independent of x and z.

[0084] Specifically, the instantaneous macroscopic quantity and the reduced distribution function are expressed as follows:

[0085] ; (5)

[0086] According to the equation of the reduced distribution function satisfied by the basic flow and ignoring the high-order terms, the small perturbation equation can be expressed as:

[0087] ; (6)

[0088] S4: According to the method of finding the moment of the distribution function, the relationship between the perturbation reduced distribution function and the perturbation macroscopic quantity is determined:

[0089] ; (7)

[0090] S5: Performing canonical modal analysis on the disturbance in the disturbance model, and obtaining the product of the shape function and the wave function in the form of:

[0091] ; (8)

[0092] In an optional embodiment of the present specification, the function of the stability model is expressed as follows:

[0093] ; (9)

[0094] S6: Using diffuse reflection boundary conditions, derive the corresponding diffuse reflection boundary conditions under the assumption of small perturbation:

[0095] ; (10)

[0096] S7: discretize the stability model and the preset boundary conditions using a specified method to obtain a target equation and a target boundary condition. The specified method in this specification includes a finite difference format and a Gauss-Hermite velocity space discretization method.

[0097] The discretized form of the target stability equation is:

[0098] ; (11)

[0099] The discrete form corresponding to the diffuse reflection boundary condition is:

[0100] ; (12)

[0101] The discrete stability equations and discrete boundary conditions can be written in the following form:

[0102] ; (13)

[0103] Where: M j,k represents a function containing the Knudsen number, N j,k Velocity as a function of wave number, L j,k represents the function of the Mach number, E jm Spectral method coefficients, and Represents the reduced distribution function of different velocity space points at the same physical space point, W l Represents the weight coefficient.

[0104] Equation (13) is a homogeneous system of equations. Therefore, in general, there are only meaningless zero solutions. When the Mach number, Knudsen number, wave number or circular frequency in the equation satisfies a certain relationship, the equation may have a non-zero solution. In classical stability theory, this relationship is called the characteristic relationship, and the parameters that satisfy the characteristic relationship are called eigenvalues. The solution of the equation is called the characteristic function, and the problem of solving the eigenvalue and characteristic function is called the eigenvalue problem. Therefore, the stability problem can be transformed into the solution of the eigenvalue problem, as follows:

[0105] ; (14)

[0106] in: represents the coefficient matrix, represents the feature vector, represents the identity matrix, Represents the eigenvalue.

[0107] The eigenvalues ​​of the generalized eigenvalue problem above can be determined by the following determinant:

[0108] ; (15)

[0109] S8: The implicit restart Arnoldi algorithm is used to solve the generalized eigenvalue problem above, and the eigenvalue and special value vector can be obtained. Each eigenvalue corresponds to a perturbation mode. When the imaginary part of the eigenvalue is greater than zero, the mode is a growth mode. When the imaginary part of the eigenvalue is less than zero, the mode is a decay mode. When the imaginary part of the eigenvalue is equal to zero, the mode is neutrally stable. The spatial distribution characteristics of the disturbance can be analyzed through the characteristic function.

[0110] S9: Compare and analyze the calculation accuracy and efficiency with the spectral method.

[0111] In this embodiment of the present invention, the method further includes:

[0112] S10: Based on the analysis results of the two-dimensional gas kinetic flow stability analysis and the shape parameters of the aircraft model, the aircraft model transition prediction results are obtained.

[0113] This method can efficiently obtain the analysis results of the two-dimensional gas kinetic flow stability analysis, and then can efficiently realize the transition prediction of high-altitude aircraft. The method of predicting the transition of the aircraft model based on the analysis results of the two-dimensional gas kinetic flow stability analysis and the aircraft model shape parameters in the present invention can adopt the existing aircraft model transition prediction method, and the embodiments of the present invention are not specifically limited, such as CN117408189A and CN114036869A.

[0114] Furthermore, the applicant also used an incompressible flat plate Couette flow example in the research process to verify the calculation accuracy and efficiency of the method in this specification. The calculation conditions used in the verification are shown in Table 1, which is a calculation condition table. The applicant used the linear stability method based on the Chebyshev spectrum method and the method of the present invention to calculate the phase velocity spectrum of the flat plate Couette flow at different Knudsen numbers when the Mach number is 0.5, in order to verify the high efficiency of the method of the present invention.

[0115] Table 1 Calculation conditions

[0116] Mach number Knudsen number Kn Streamwise wave number α 0.5 0.0001 0.5 0.5 0.01 3.0

[0117] Figure 2 and Figure 3 The calculation results of phase velocity spectra under different Knudsen numbers using the spectral method and the method of the present invention are shown in Figure 2. Figure 2 and3 It can be seen from the figure that the results obtained by the two calculation methods are in good agreement, thus verifying the correctness of the method in the present invention.

[0118] In order to verify the calculation accuracy and efficiency of the method in this specification, the spectral method and the method in the present invention are used to compare the most unstable mode eigenvalues ​​and calculation time under different Knudsen numbers, as shown in Table 2. Table 2 shows the most unstable mode growth rate and calculation time table obtained in different numerical formats. It is not difficult to find that the calculation accuracy of the method in the present invention is one ten-thousandth different from the result of the spectral method, while the calculation time is shortened by nearly three times at most.

[0119] Table 2 The most unstable mode growth rate and calculation time table obtained by different numerical formats

[0120] Knudsen number Kn Growth rate (finite difference) Growth rate (spectral method) Relative deviation Computation time (finite differences) Computation time (spectral method) 0.0001 -0.123085715328987i -0.123078784990908i 0.006% 4.408 9.503 0.01 -0.538009743918603i -0.538139218441535i 0.024% 26.865 79.529

[0121] Among them, the modal eigenvalue is a complex number, the growth rate is the imaginary part of the modal eigenvalue, and i in Table 2 is the imaginary unit. Figure 2-Figure 3 The phase velocity is the real part of the mode eigenvalue and has no units.

[0122] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0123] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A two-dimensional gas kinetic flow stability analysis method based on a finite difference format, characterized in that: The method comprises: Step 1: Select the BGK model as the initial model; Step 2: introducing a reduced distribution function, eliminating the dependence of the distribution function on the molecular velocity in the vertical direction in the initial model, and obtaining a model of the reduced distribution function; Step 3: Under the condition that the rarefied gas satisfies the parallelism hypothesis and the small perturbation hypothesis, the instantaneous quantity in the model about the reduced distribution function is rewritten into the form of the sum of the basic flow and the perturbation quantity; under the condition that the basic flow satisfies the model about the reduced distribution function, the small perturbation equation is obtained; Step 4: Process the perturbation reduced distribution function in the small perturbation equation by moment calculation to obtain the relationship between the perturbation reduced distribution function and the perturbation macroscopic quantity; Step 5: Write the disturbance in the small disturbance equation as the product of the shape function and the wave function to obtain the stability equation; Step 6: Using diffuse reflection boundary conditions, derive the diffuse reflection boundary conditions corresponding to the disturbance under the assumption of small disturbance; Step 7: Based on the relationship between the disturbance reduced distribution function and the disturbance macroscopic quantity, the stability equation and the boundary conditions of the disturbance are discretized to obtain the target equation and target boundary conditions; Step 8: solving eigenvalues ​​and eigenvectors based on the target equation, the target boundary conditions and given parameters, and obtaining analysis results of two-dimensional gas kinetic flow stability analysis based on the solution results of the eigenvalues ​​and eigenvectors; The diffuse reflection boundary condition corresponding to the disturbance is: ； in: represents the reduced perturbation distribution function on the particle boundary, r w represents the position on the particle boundary, h Indicates the time interval, represents the equilibrium perturbation distribution function on the particle boundary, ρ w represents the boundary perturbation density, u w represents the average velocity of the streamwise disturbance on the boundary, n represents the normal vector of the boundary, t Indicates time, ξ represents the particle velocity; ρ w It is expressed as: ； in, represents the equilibrium perturbation distribution function on the particle boundary; It is expressed as: ； in, R represents the particle equilibrium constant, ξ x and ξ y are the particle velocities in the streamwise and normal directions, respectively; The discrete form of the stability equation is: ； in, N Indicates the number of physical space points, j Indicates the current point in physical space. represents the finite difference scheme coefficients, i is an imaginary number, a is the wave number, K is the Knudsen number, for ρ The basic amount, Indicates the point in velocity space k The normal discrete particle velocity, Represents a point in physical space p Speed ​​Space Point k The reduced perturbation distribution function of Indicates the point in velocity space k The particle velocity of the stream, Represents a point in physical space j Speed ​​Space Point k The reduced perturbation distribution function of Represents a point in physical space j Speed ​​Space Point k The basic quantity of the equilibrium distribution function, Represents a point in physical space j Speed ​​Space Point k The basic quantity of the reduced distribution function, W l represents the weight coefficient, Q represents a velocity space point, Represents a point in physical space j Speed ​​Space Point l The reduced perturbation distribution function of Represents a point in physical space j Flow to macro velocity, Represents a velocity space point l The particle velocity of the stream, Represents a velocity space point l The normal particle velocity; The discrete form corresponding to the perturbed boundary condition is: ； in, represents the velocity space point on the boundary k Reduced perturbation distribution function, represents the velocity space point on the boundary k The basic quantity of the reduced perturbation equilibrium distribution function, The basic quantity representing the distribution function of the reduced perturbation equilibrium state that satisfies the molecular velocity condition on the boundary, W up is the upper surface integral weight coefficient, W low is the integral weight coefficient of the lower surface, represents the reduced perturbation distribution function on the boundary, represents the boundary point, ρ c is the basic quantity of density, ξ y is the particle velocity in the normal direction.

2. The two-dimensional gas kinetic flow stability analysis method based on finite difference format according to claim 1 is characterized in that: The initial two-dimensional BGK model is: ； in, f = f ( t , x , y , ξ x , ξ y , ξ z ) represents the distribution function of particles with respect to time, physical space and velocity space, x Indicates the flow direction, y represents the normal direction, ξ x , ξ y and ξ z are the particle velocities in the streamwise, normal and spanwise directions, respectively. t Indicates time, a x represents the acceleration in the flow direction, T Indicates temperature, ρ is the density, f e The particle equilibrium distribution function, K is the Knudsen number, μ Indicates viscosity.

3. The two-dimensional gas kinetic flow stability analysis method based on finite difference format according to claim 2 is characterized in that: The reduced distribution function is: ； in: g ( t , x , y , ξ x , ξ y )= g is the reduced distribution function; The reduced distribution function is introduced into the model equation: ； in: g e represents the particle reduced equilibrium distribution function; ； in, ξ =( ξ x , ξ y ) represents the particle velocity, u =( u , v ) represents the macroscopic speed, u is the flow velocity, v is the normal velocity, R represents the particle equilibrium constant.

4. The two-dimensional gas kinetic flow stability analysis method based on finite difference format according to claim 1 is characterized in that: Under the condition that the rarefied gas satisfies the parallelism assumption and the small disturbance assumption, the instantaneous quantity in the model of the reduced distribution function is rewritten as the sum of the basic flow and the disturbance quantity, including: ； in, t Indicates time, x Indicates the flow direction, y represents the normal direction, ξ x and ξ y are the particle velocities in the streamwise and normal directions, respectively, u is the flow velocity, v is the normal velocity, for g The basic amount, for g The disturbance amount, g e represents the particle reduced equilibrium distribution function, for g e The basic amount, for g e The disturbance amount, ρ is the density, for ρ The basic amount, for ρ The disturbance amount, for u The basic amount, for u The disturbance amount, v The basic amount is 0, for v The amount of disturbance; The small perturbation equation is initially constructed as: ； Eliminating the basic flow term and nonlinear term, the small perturbation equation is obtained: ； in, a x represents the acceleration in the flow direction, K is the Knudsen number, R represents the particle equilibrium constant.

5. The two-dimensional gas kinetic flow stability analysis method based on finite difference format according to claim 4 is characterized in that: The perturbation in the small perturbation equation is written as the product of the shape function and the wave function, specifically: ； in, e is the natural base, i is an imaginary number, a is the wave number, is the frequency, for ρ The amplitude of for g The amplitude of for u The amplitude of for v The amplitude of for g e The amplitude of The stability equation is: 。 6. The two-dimensional gas kinetic flow stability analysis method based on finite difference format according to claim 4 is characterized in that: The perturbation-reduced distribution function in the small perturbation equation is processed by moment calculation to obtain the relationship between the perturbation-reduced distribution function and the perturbation macroscopic quantity, which is: ;in, ξ Represents the particle speed.

7. The two-dimensional gas kinetic flow stability analysis method based on finite difference format according to claim 1 is characterized in that: After step 8, the method further comprises: Based on the analysis results of two-dimensional gas kinetic flow stability analysis and the shape parameters of the aircraft model, the transition prediction results of the aircraft model are obtained.

Images