An efficient numerical method for simulating near-space vehicle cross-basin flows

Abstract

This paper proposes an efficient numerical method for simulating cross-basin flows of near-space vehicles. The method sequentially generates physical and velocity space grids based on vehicle geometry and incoming flow parameters, sets initial flow field variables, calculates interface fluxes, implicitly solves macroscopic adjoint equations to obtain estimated macroscopic quantities, implicitly solves the Boltzmann equation to obtain the distribution function for the next iteration, and uses the distribution function to update the flow field variables, achieving iterative flow field calculations. By coupling the implicit solution of the Boltzmann equation with the corresponding macroscopic governing equations and constructing multi-scale macroscopic fluxes, the method improves the efficiency of cross-basin flow simulations while maintaining simulation accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of computational fluid dynamics, and in particular to an efficient numerical method for simulating cross-basin flow of near-space aircraft. Background Art

[0002] The airspace between 20 and 80 kilometers, known as near-space, holds immense strategic value. Countries around the world are vying to conduct research on high-speed aircraft, including spacecraft, deep-space exploration vehicles, and near-space vehicles. Within this range, due to the high speeds of aircraft (typically exceeding Mach 5), the windward gas is highly compressed, resulting in a flow pattern characterized by a continuous flow basin. The leeward gas, on the other hand, experiences a dramatic expansion, often exhibiting a rarefied flow basin. The overall flow field exhibits distinct cross-basin motion.

[0003] To accurately capture the motion characteristics of near-space vehicles within this airspace, traditional single numerical solution methods are insufficient. Data derived from the Navier-Stokes (NS) equations exhibit significant errors in the leeward region, while the Direct Simulation Monte Carlo (DSMC) method consumes significant computational resources when simulating the flow field near the upwind region. To address these issues, researchers have proposed a series of multiscale solution methods based on a discrete velocity framework, such as the Gas Kinetic Unified Algorithm (GKUA), the Unified Gas Kinetic Scheme (UGKS), and the Discrete Unified Gas Kinetic Scheme (DUGKS). These methods utilize a unified computational framework, eliminating the need for manually setting overlap zones for data transfer between different methods. This allows for full-basin flow simulation, providing support for modeling cross-basin flows. However, these methods suffer from a significant drawback: low computational efficiency. To accurately simulate interbasin flows, multiscale solutions based on a discrete velocity framework require not only discretization in time and physical space, but also in particle velocity space. This results in computational resources far exceeding those required for traditional solutions to the NS equations. Therefore, improving the computational efficiency of these methods is an urgent issue. Summary of the Invention

[0004] In order to solve the problems existing in the existing technology and realize the rapid prediction of the cross-basin flow field of near-space aircraft, the present invention proposes an efficient numerical method for simulating the cross-basin flow of near-space aircraft. The method is based on a discrete velocity framework and can quickly solve the Boltzmann equation and the corresponding macroscopic adjoint equation, thereby improving the simulation efficiency of the cross-basin flow problem of near-space aircraft.

[0005] The technical solution of the present invention is:

[0006] An efficient numerical method for simulating the flow of near-space vehicles across a watershed includes the following steps:

[0007] Step 1: Generate physical space grid and velocity space grid based on the aircraft geometry parameters and incoming flow parameters in combination with the simulation conditions;

[0008] Step 2: Set the flow field variables at the initial moment;

[0009] Step 3: Calculate interfacial fluxes, including macroscopic fluxes and the distribution function flux

[0010] Distribution function flux The calculation formula is

[0011]

[0012] in represents the distribution function flux numbered k at the interface ij, is the distribution function numbered k at the interface ij, is the distribution function The particle velocity of the described particle, is the unit normal vector of the interface ij, pointing from unit i to unit j, as well as Represent the spatial coordinates of the center of interface ij, the center of unit i, and the center of unit j, respectively. and are the gradients of the distribution function numbered k at the center of unit i and the center of unit j respectively;

[0013] Macro flux The calculation formula is

[0014]

[0015] in represents the macroscopic flux at the interface ij, represents the macroscopic flux obtained by numerical integration of the interface distribution function, represents the macroscopic flux obtained by macroscopic calculation, represents the relaxation time calculated based on the macroscopic quantity of the interface, h ij represents the local time step;

[0016] Step 4: Using the macroscopic flux obtained in step 3, implicitly solve the macroscopic adjoint equation to obtain the estimated macroscopic quantity;

[0017] Step 5: Using the estimated macroscopic quantities obtained in step 4 and the distribution function flux obtained in step 3, implicitly solve the Boltzmann equation to obtain the distribution function for the next iteration step;

[0018] Step 6: Update the flow field variables using the distribution function;

[0019] Step 7: Determine whether the flow field has converged. If so, proceed to step 8; if not, return to step 3.

[0020] Step 8: Post-process the calculation results to obtain the cloud map of flow field related parameters.

[0021] In a further preferred embodiment, in step 3, the local time step is determined by the following formula:

[0022]

[0023] h ij =min(h i ,h j ),h i =δt i CFL phys

[0024] Where V i is the volume of unit i, N(i) is the set of units adjacent to unit i, k represents the number of the distribution function, A ij is the area of ​​the interface ij, δt i 、h i and h j For temporary variables, CFL phys is the number of CFLs that meet the stability conditions.

[0025] In a further preferred embodiment, in step 3, Decomposed into balanced flux and unbalanced flux:

[0026]

[0027] in To balance the flux, is the non-equilibrium flux, and the two are calculated by the following formulas:

[0028]

[0029] in are the relevant motion variables of the particle, is the particle's velocity, is the rotational speed of the particle, is the velocity space differential, T t is the translational temperature, as well as Represent the pressure at the interface ij close to the unit i and unit j, respectively. as well as represent the density, momentum density, total energy density and rotational energy density at the interface ij, respectively. represents the macroscopic quantity at the interface, and represent the macroscopic quantities at the center of unit i and unit j respectively, and Represent the macroscopic gradients of the centers of unit i and unit j, respectively. Represents interface macroscopic quantity The corresponding equilibrium distribution function, f i is the distribution function set of the center of unit i, F i * is the equilibrium distribution function set of the center of unit i, is the distribution function of unit i with number k at the center, The relevant motion variables obtained by calculating the particle velocity of the distribution function numbered k, is the macroscopic quantity obtained by numerically integrating all the distribution functions at the center of unit i, To pass The calculated equilibrium distribution function set.

[0030] In a further preferred embodiment, the process of implicitly solving the macroscopic adjoint equation in step 4 is as follows:

[0031] The macroscopic adjoint equation is

[0032]

[0033] in, is the macroscopic increment of the center of unit i at time n+1, is the estimated macroscopic quantity of the center of unit i at time n+1, V i is the volume of unit i, is the macroscopic flux at the interface ij at time n+1, is the source term at the center of the unit at time n+1; the expression of Δt is

[0034]

[0035] CFL is the CFL number of the implicit method;

[0036] The macroscopic adjoint equation is organized into the following form

[0037]

[0038] And use point relaxation symmetric Gauss-Seidel iteration to solve, that is

[0039] Forward scan:

[0040]

[0041] Backward scan:

[0042]

[0043] When the macro increment of unit i is obtained Afterwards, through Get the estimated macro quantity of unit i at time n+1.

[0044] In a further preferred embodiment, in step 4:

[0045] The expression is

[0046]

[0047] γ is the specific heat ratio, R is the gas constant, T t,ij is the translational temperature at the interface ij, μ ij is the dynamic viscosity coefficient at the interface ij, μ ref is the reference dynamic viscosity coefficient, T ref is the reference temperature, ω is the power exponent;

[0048] The expression is

[0049]

[0050] is the rotational energy density at the center of unit i, The increment of the rotational energy density at the center of unit i, Z is the number of rotational collisions, and K is the internal degree of freedom of the molecule.

[0051] In a further preferred embodiment, in step 5, the process of implicitly solving the Boltzmann equation is:

[0052] The implicit governing equation solved by the Boltzmann equation is

[0053]

[0054] in represents the increment of the distribution function of unit i with center number k, The increment of the distribution function of the interface ij numbered k, represents the equilibrium distribution function of unit i with center number k, represents the relaxation time of the center of unit i;

[0055] The implicit control equation is organized into the following form:

[0056]

[0057] And use point relaxation symmetric Gauss-Seidel iteration to solve, that is

[0058] Forward scan:

[0059]

[0060] Backward scan:

[0061]

[0062] When the macro increment of unit i is obtained Afterwards, through Obtain the distribution function of unit i at time n+1 numbered k.

[0063] In a further preferred embodiment, in step 5, The calculation formula is

[0064]

[0065]

[0066] In a further preferred embodiment, the process of updating the flow field variables using the distribution function in step 6 is as follows:

[0067] After obtaining the distribution function at time n+1, the macro variables at time n+1 are updated as follows:

[0068]

[0069] At this point, the calculation of one iteration step is completed.

[0070] In a further preferred solution, step 7 uses the velocity two-norm error as the convergence criterion, and the criterion formula is:

[0071]

[0072] in represents the velocity field of the reference iteration step, represents the velocity field n iteration steps away from the reference iteration step, and ε is the convergence threshold.

[0073] Beneficial effects

[0074] Aiming at the demand for predicting the cross-basin flow field of near-space aircraft, the present invention proposes an efficient numerical method for simulating the cross-basin flow of near-space aircraft. By adopting the means of coupling implicit solution of the Boltzmann equation and the corresponding macro-control equation and constructing multi-scale macro-fluxes, the simulation efficiency of the cross-basin flow problem is improved while maintaining the simulation accuracy.

[0075] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which:

[0077] Figure 1 :Flowchart of near-space vehicle cross-basin flow simulation;

[0078] Figure 2 : The physical space mesh and surface mesh used by the X-38 aircraft (a total of 240,308 units, 1,365 units of surface mesh); (a) physical space mesh, (b) surface mesh;

[0079] Figure 3 : Velocity space grid used by the X-38 aircraft (34545 cells in total);

[0080] Figure 4 : Schematic diagram of implicit solution of control equations;

[0081] Figure 5 :Distribution of physical quantities of the flow field near the X-38 aircraft; (a) density cloud map, (b) pressure cloud map, (c) equilibrium temperature cloud map, (d) rotational temperature cloud map;

[0082] Figure 6 :Surface pressure coefficient and heat flux coefficient distribution of X-38 aircraft; (a) pressure coefficient distribution, (b) heat flux coefficient distribution;

[0083] Figure 7 : Pressure coefficient distribution and heat flux coefficient distribution on the symmetrical surface of the X-38 aircraft; (a) pressure coefficient distribution, (b) heat flux coefficient distribution. DETAILED DESCRIPTION

[0084] The following describes in detail embodiments of the present invention. The embodiments are exemplary and intended to explain the present invention, but are not to be construed as limiting the present invention.

[0085] This embodiment takes the X-38 near-space aircraft as an example to perform numerical simulation of the flow around the X-38 near-space aircraft. The simulated working conditions are Ma=8.0, Kn=0.0275, and the flight angle of attack is 20°. Figure 1 As shown, this embodiment provides an efficient numerical method for simulating near-space vehicle cross-basin flow. The calculation of the interface flux in red and the order of solving the Boltzmann equation and the corresponding macroscopic adjoint equation in the red box are key technologies of the present invention. The specific steps of this cross-basin flow simulation method include:

[0086] Step 1: Generate the following parameters based on the aircraft geometry parameters and the incoming flow parameters, combined with the simulation conditions: Figure 2 The physical space grid shown (240,308 cells total, 1,365 cells on the surface grid) and Figure 3 Velocity space grid shown (34,545 cells total).

[0087] Step 2: Set the initial flow field variables. In this embodiment, based on the set simulation conditions, the parameters of the entire flow field are set to the incoming flow parameters during initialization, and the distribution function is initialized to the equilibrium distribution function. The distribution function is a key concept that describes the distribution of gas particles in phase space and represents the number density of particles with a specific velocity at a certain time and location.

[0088] Step 3: Calculate interfacial fluxes, including macroscopic fluxes and the distribution function flux

[0089] Distribution function flux The calculation is

[0090]

[0091] in represents the distribution function flux numbered k at the interface ij (the interface between unit i and unit j), is the distribution function numbered k at the interface ij, is the distribution function The particle velocity of the described particle, is the unit normal vector of the interface ij, pointing from unit i to unit j, as well as Represent the spatial coordinates of the center of interface ij, the center of unit i, and the center of unit j, respectively. and are the gradients of the distribution function numbered k at the center of unit i and the center of unit j respectively.

[0092] Before solving the macroscopic adjoint equation, it is necessary to obtain the macroscopic flux of the interface The interface is the surface that constitutes the finite volume unit. Under the premise of ensuring that the macroscopic flux of the interface is applicable in the entire flow basin, this embodiment chooses to use a weighted form to obtain the macroscopic flux at the interface, that is,

[0093]

[0094] in represents the macroscopic flux at the interface ij, represents the macroscopic flux obtained by numerical integration of the interface distribution function, represents the macroscopic flux obtained by calculating macroscopic quantities (such as density, momentum, energy, etc.), represents the relaxation time calculated based on the macroscopic quantity of the interface, h ij Represents the local (interface ij) time step, and this parameter is determined by the following formula:

[0095]

[0096] Where V i is the volume of unit i, N(i) is the set of units adjacent to unit i, k represents the number of the distribution function, A ij is the area of ​​the interface ij, δt i 、h i and h j To facilitate the calculation of h ij The temporary variable defined, CFL phys The number of CFLs required to meet the stability conditions is usually less than 1.

[0097] In formula (2) The distribution function at the interface used in can be obtained by spatial reconstruction, and in order to improve the stability of the algorithm, It is decomposed into equilibrium flux and non-equilibrium flux, that is,

[0098]

[0099] in To balance the flux, is the non-equilibrium flux, and the two are calculated by the following formulas, where When you need to use as well as The calculations of the two are consistent with the macroscopic quantities at the interface ( as well as ), so it is necessary to give a calculation formula for the macroscopic quantities at the interface.

[0100]

[0101] is the relevant motion variable of the particle, that is is the particle's velocity, is the rotational speed of the particle, is the velocity space differential, T t is the translational temperature, as well as Represents the pressure at the interface ij close to the unit i and unit j side (through the translation temperature T t calculate), as well as represent the density, momentum density, total energy density and rotational energy density at the interface ij, respectively. represents the macroscopic quantity at the interface, and Represent the macroscopic quantities at the center of unit i and unit j, including density, momentum density, total energy density and rotational energy density, and Represent the macroscopic gradients of the centers of unit i and unit j, respectively. Represents interface macroscopic quantity The corresponding equilibrium distribution function, f i is the distribution function set of the center of unit i, F i * is the equilibrium distribution function set of the center of unit i (through the macroscopic quantity of the center of unit i Calculated), is the distribution function of unit i with number k at the center, The relevant motion variables obtained by calculating the particle velocity of the distribution function numbered k, is the macroscopic quantity obtained by numerically integrating all the distribution functions at the center of unit i (due to the existence of integration error, and There are certain errors between them). To pass The calculated equilibrium distribution function set.

[0102] Combining equations (1)-(6) yields a macroscopic flux that is applicable across the entire basin, significantly simplifying the computational effort. The distribution function flux can be simply calculated by directly using spatial reconstruction to obtain the distribution function of the unit interface. This indicates that the greatest computational effort in current methods for calculating interface fluxes lies in spatial reconstruction, which is significantly simplified compared to UGKS and DUGKS.

[0103] If an explicit method is used to solve the Boltzmann equation, the problem of "small time advancement step and low computational efficiency" cannot be solved. Therefore, a fully implicit method is used to solve it in the present invention. At this time, how to obtain the equilibrium distribution function that appears in the right-hand collision term in the n+1 iteration step is a key issue. The right-hand collision term refers to the term on the right side of the Boltzmann equation's equal sign. Because this term represents the collision of particles, it is referred to as the "right-hand collision term" here. The equilibrium distribution function is related to macroscopic quantities, and macroscopic quantities are obtained by numerical integration of distribution functions in discrete velocity methods. Therefore, there is a strong coupling effect between the two. If an accurate solution is to be obtained, a huge amount of calculation is involved. For this reason, in the present invention, an estimated macroscopic quantity is first obtained by implicitly solving the corresponding macroscopic adjoint equation. Then, the equilibrium distribution function corresponding to the estimated macroscopic quantity is substituted into the right-hand term in the Boltzmann equation, which greatly simplifies the amount of calculation. The solution accuracy of the estimated macroscopic quantity will affect the efficiency of implicitly solving the Boltzmann equation. Therefore, the construction of multi-scale macroscopic flux in the present invention is the key to affecting the efficiency of the entire algorithm solution. In addition, since the discrete velocity method has a huge demand for computing memory, in order to save memory requirements, point relaxation symmetric Gauss-Seidel iteration is used when implicitly solving the control equations to reduce the additional memory consumption caused by implicit solution. The calculation diagram of this process is shown in the figure below. Figure 4 shown.

[0104] Step 4: Using the macroscopic flux obtained in step 3, implicitly solve the macroscopic adjoint equation to obtain the estimated macroscopic quantity.

[0105] The macroscopic adjoint equation that needs to be solved by this method is

[0106]

[0107] in, is the macroscopic increment of the center of unit i at time n+1, is the estimated macroscopic quantity of the center of unit i at time n+1, V i is the volume of unit i, is the macroscopic flux at the interface ij (the interface between unit i and unit j) at time n+1, is the source term at the center of the unit at time n+1. The expression of Δt is

[0108]

[0109] δt i The calculation formula is the same as formula (3), CFL is the CFL number of the implicit method, which is usually not limited and is usually set to (10~10000)×CFL phys .

[0110] The expression is

[0111]

[0112] γ is the specific heat ratio. For diatomic molecular gases (such as nitrogen), γ = 1.4. R is the gas constant, T t,ij is the translational temperature at the interface ij, μ ij is the dynamic viscosity coefficient at the interface ij, μ ref is the reference dynamic viscosity coefficient, T ref is the reference temperature, and both are usually set as the incoming flow parameters. ω is the power exponent, and for nitrogen, ω is usually set to 0.74.

[0113] The expression is

[0114]

[0115] is the rotational energy density at the center of unit i, The rotational energy density increment at the center of cell i. Z is the number of rotational collisions, which is set according to different calculation conditions. K is the internal degree of freedom of the molecule. For diatomic molecular gases (such as nitrogen), K = 2.

[0116] Using the above formula, formula (7) can be organized into the following form, namely

[0117]

[0118] After obtaining formula (11), the point relaxation symmetric Gauss-Seidel iteration can be used to solve it, that is,

[0119] Forward scan:

[0120]

[0121] Backward scan:

[0122]

[0123] According to experience, m = 2 is usually sufficient to meet the requirements of most examples. Afterwards, through Get the estimated macro quantity of unit i at time n+1.

[0124] Step 5: Using the estimated macroscopic quantities obtained in step 4 and the distribution function flux obtained in step 3, implicitly solve the Boltzmann equation to obtain the distribution function for the next iteration step;

[0125] The implicit governing equation solved by the Boltzmann equation is

[0126]

[0127] in represents the increment of the distribution function of unit i with center number k, The increment of the distribution function of the interface ij numbered k, Represents the equilibrium distribution function of unit i with center number k (through Calculated), represents the relaxation time at the center of unit i. The calculation formula is

[0128]

[0129] Using the above formula, formula (14) can be organized into the following form, that is,

[0130]

[0131] After obtaining formula (16), the point relaxation symmetric Gauss-Seidel iteration can be used to solve it, that is,

[0132] Forward scan:

[0133]

[0134] Backward scan:

[0135]

[0136] According to experience, m = 2 is usually sufficient to meet the requirements of most examples. Afterwards, through Obtain the distribution function of unit i at time n+1 numbered k.

[0137] Step 6: Update the flow field variables using the distribution function.

[0138] After obtaining the distribution function at time n+1, the macro variables at time n+1 are updated as follows:

[0139]

[0140] At this point, the calculation of one iteration step is completed.

[0141] Step 7: Determine whether the flow field has converged. If it has converged, proceed to step 8; if it has not converged, go back to step 3. Generally, the velocity norm error is used as the convergence criterion, and the criterion formula is:

[0142]

[0143] in represents the velocity field of the reference iteration step, represents the velocity field n iterations away from the reference iteration step, and ε is the convergence threshold. Assuming the current iteration step is step and the reference iteration step is set to n iterations away from the current iteration step, the reference iteration step is step – n, where n is a manually set value, set to 100 in this example.

[0144] Step 8: Post-process the calculation results, such as obtaining density cloud maps, pressure cloud maps, equilibrium temperature cloud maps, and rotational temperature cloud maps.

[0145] Figure 5 The density cloud map, pressure cloud map, equilibrium temperature cloud map and rotation temperature cloud map obtained by the current method simulation are shown. Figure 6 The pressure coefficient distribution and heat flux coefficient distribution on the surface of the X-38 aircraft are shown. In order to verify the correctness of the current method, Figure 7 The distribution of pressure and heat flux coefficients on the symmetric surfaces of the X-38 aircraft is presented and compared with simulation results using the classic DSMC algorithm. The results show good agreement between the current algorithm and the DSMC method. Table 1 shows the lift and drag coefficients calculated by the current and DSMC methods, demonstrating that the error between the current and DSMC methods is within 5%. Table 2 shows the computational resources consumed by the current and DSMC methods for simulating the current operating conditions on the same computing platform. The results demonstrate a clear advantage in computational efficiency over the current method.

[0146] Table 1 Comparison of lift and drag coefficients experienced by the aircraft in the X-38 aircraft flow calculation example

[0147]

[0148] Table 2 Comparison of computational resource consumption of different methods in the X-38 aircraft flow example

[0149]

[0150] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. An efficient numerical method for simulating near-space vehicle cross-basin flows, characterized by: The following steps are involved: Step 1: Generate physical space grid and velocity space grid based on the aircraft geometry parameters and incoming flow parameters in combination with the simulation conditions; Step 2: Set the flow field variables at the initial moment; Step 3: Calculate interfacial fluxes, including macroscopic fluxes and the distribution function flux Distribution function flux The calculation formula is in represents the distribution function flux numbered k at the interface ij, is the distribution function numbered k at the interface ij, is the distribution function The particle velocity of the described particle, is the unit normal vector of the interface ij, pointing from unit i to unit j, as well as Represent the spatial coordinates of the center of interface ij, the center of unit i, and the center of unit j, respectively. and are the gradients of the distribution function numbered k at the center of unit i and the center of unit j respectively; Macro flux The calculation formula is in represents the macroscopic flux at the interface ij, represents the macroscopic flux obtained by numerical integration of the interface distribution function, represents the macroscopic flux obtained by macroscopic calculation, represents the relaxation time calculated based on the macroscopic quantity of the interface, h ij represents the local time step; Step 4: Using the macroscopic flux obtained in step 3, implicitly solve the macroscopic adjoint equation to obtain the estimated macroscopic quantity; Step 5: Using the estimated macroscopic quantities obtained in step 4 and the distribution function flux obtained in step 3, implicitly solve the Boltzmann equation to obtain the distribution function for the next iteration step; Step 6: Update the flow field variables using the distribution function; Step 7: Determine whether the flow field converges; if so, proceed to step 8; if not, return to step 3; Step 8: Post-process the calculation results to obtain the cloud map of flow field related parameters.

2. The efficient numerical method for simulating near-space vehicle cross-basin flow according to claim 1, characterized in that: In step 3, the local time step is determined by the following formula: h ij =min(h i ,h j ),h i =δt i ·CFL phys Where V i is the volume of unit i, N(i) is the set of units adjacent to unit i, k represents the number of the distribution function, A ij is the area of ​​the interface ij, δt i 、h i and h j For temporary variables, CFL phys is the number of CFLs that meet the stability conditions.

3. The efficient numerical method for simulating near-space vehicle cross-basin flow according to claim 1, characterized in that: In step 3, Decomposed into balanced flux and unbalanced flux: in To balance the flux, is the non-equilibrium flux, and the two are calculated by the following formulas: in are the relevant motion variables of the particles, is the particle's velocity, is the rotational speed of the particle, is the velocity space differential, T t is the translational temperature, as well as Represent the pressure at the interface ij close to the unit i and unit j, respectively. as well as represent the density, momentum density, total energy density and rotational energy density at the interface ij, respectively. represents the macroscopic quantity at the interface, and represent the macroscopic quantities at the center of unit i and unit j respectively, and Represent the macroscopic gradients of the centers of unit i and unit j, respectively. Represents interface macroscopic quantity The corresponding equilibrium distribution function, f i is the set of distribution functions of the center of unit i, is the equilibrium distribution function set of the center of unit i, is the distribution function of unit i with number k at the center, The relevant motion variables obtained by calculating the particle velocity of the distribution function numbered k, is the macroscopic quantity obtained by numerically integrating all the distribution functions at the center of unit i, To pass The calculated equilibrium distribution function set.

4. The efficient numerical method for simulating near-space vehicle cross-basin flow according to claim 1, characterized in that: The implicit solution process of the macroscopic adjoint equation in step 4 is: The macroscopic adjoint equation is in, is the macroscopic increment of the center of unit i at time n+1, is the estimated macroscopic quantity of the center of unit i at time n+1, V i is the volume of unit i, is the macroscopic flux at the interface ij at time n+1, is the source term at the center of the unit at time n+1; the expression of Δt is CFL is the CFL number of the implicit method; The macroscopic adjoint equation is organized into the following form And use point relaxation symmetric Gauss-Seidel iteration to solve, that is Forward scan: Backward scan: When the macro increment of unit i is obtained Afterwards, through Get the estimated macro quantity of unit i at time n+1.

5. The efficient numerical method for simulating near-space vehicle cross-basin flow according to claim 4, characterized in that: In step 4: The expression is γ is the specific heat ratio, R is the gas constant, T t,ij is the translational temperature at the interface ij, μ ij is the dynamic viscosity coefficient at the interface ij, μ ref is the reference dynamic viscosity coefficient, T ref is the reference temperature, ω is the power exponent; The expression is is the rotational energy density at the center of unit i, The increment of the rotational energy density at the center of unit i, Z is the number of rotational collisions, and K is the internal degree of freedom of the molecule.

6. The efficient numerical method for simulating near-space vehicle cross-basin flow according to claim 1, characterized in that: In step 5, the process of implicitly solving the Boltzmann equation is: The implicit governing equation solved by the Boltzmann equation is in represents the increment of the distribution function of unit i with center number k, The increment of the distribution function of the interface ij numbered k, represents the equilibrium distribution function of unit i with center number k, represents the relaxation time of the center of unit i; The implicit control equation is organized into the following form: And use point relaxation symmetric Gauss-Seidel iteration to solve, that is Forward scan: Backward scan: When the macro increment of unit i is obtained Afterwards, through Obtain the distribution function of unit i at time n+1 numbered k.

7. The efficient numerical method for simulating near-space vehicle cross-basin flow according to claim 6, characterized in that: In step 5, The calculation formula is 8. The efficient numerical method for simulating near-space vehicle cross-basin flow according to claim 1, characterized in that: The process of using the distribution function to update the flow field variables in step 6 is as follows: After obtaining the distribution function at time n+1, the macro variables at time n+1 are updated as follows: At this point, the calculation of one iteration step is completed.

9. The efficient numerical method for simulating near-space vehicle cross-basin flow according to claim 1, characterized in that: Step 7 uses the velocity two-norm error as the convergence criterion, and the criterion formula is: in represents the velocity field of the reference iteration step, represents the velocity field n iteration steps away from the reference iteration step, and ε is the convergence threshold.

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