Efficient numerical method for simulating inter-basin flow of near space aircraft

Abstract

The invention provides an efficient numerical method for simulating inter-basin flow of a near space aircraft, which sequentially comprises the following steps of: generating a physical space grid and a speed space grid according to geometric shape parameters and incoming flow parameters of the aircraft, setting a flow field variable at an initial moment, calculating interface flux, and performing implicit solution on a macroscopic adjoint equation, so as to simulate the inter-basin flow of the near space aircraft. The method comprises the following steps: obtaining a pre-estimated macroscopic quantity, carrying out implicit solution on a Boltzmann equation to obtain a distribution function of a next iteration step, and updating a flow field variable by using the distribution function to realize flow field iterative calculation. According to the method, the Boltzmann equation and the corresponding macroscopic control equation are solved in a coupling implicit mode, and the means of multi-scale macroscopic flux is constructed, so that the simulation efficiency of the cross-basin flow problem is improved while the simulation precision is kept.

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 of 20-80km is called near-space, which has extremely high strategic value. Countries around the world are competing to carry out research on high-speed aircraft such as round-trip spacecraft, deep space exploration aircraft and near-space aircraft. Within this range, due to the high flight speed of the aircraft (usually higher than Mach 5), the gas in the windward area is highly compressed, and this area mostly shows the flow characteristics of a continuous flow basin, while the gas in the leeward area expands violently, mostly showing the flow characteristics of a rarefied flow basin, and the entire flow field shows obvious cross-basin movement characteristics.

[0003] In order to accurately capture the motion characteristics of near-space aircraft in this airspace, the traditional single numerical solution method cannot meet the requirements. The relevant data solved based on the Navier-Stokes (NS) equations have large errors in the leeward area, and the Direct Simulation Monte Carlo (DSMC) method requires huge computing resources when simulating the flow field near the windward area. To solve the above problems, some researchers have proposed a series of multi-scale solution methods based on discrete velocity frameworks, such as the Gas Kinetic Unified Algorithm (GKUA), the Unified Gas Kinetic Scheme (UGKS), and the Discrete Unified Gas Kinetic Scheme (DUGKS). This type of method uses a unified computing framework, does not require artificially setting the overlap area for data transfer between different methods, realizes the simulation of the flow in the entire basin, and provides a methodological support for simulating cross-basin flow problems. However, this type of method has a significant disadvantage: low computational efficiency. In order to accurately simulate cross-basin flow problems, multi-scale solution methods based on the discrete velocity framework need to be discretized not only in time and physical space, but also in particle velocity space. This means that the computing resources required to solve such methods far exceed the computing resources required for solving the traditional NS equations. Therefore, how to improve the computational efficiency of such methods is an urgent problem to be solved. Summary of the invention

[0004] In order to solve the problems existing in the prior art 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 near-space vehicle cross-basin flow 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 combined with 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 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 interface macroscopic quantity, h ij Represents local time steps;

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

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

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

[0019] Step 7: Determine whether the flow field converges. If it converges, proceed to step 8; if it does not converge, go back 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 is a temporary variable, 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 spatial differential of velocity, 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 the 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 set of equilibrium distribution functions at the center of unit i, is the distribution function of unit i with number k at its 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:

[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 macro 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 quantities 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 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 numbered k at time n+1.

[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 embodiment, step 7 uses the velocity second norm error as the convergence criterion, and the criterion formula is:

[0071]

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

[0073] Beneficial Effects

[0074] Aiming at the demand for cross-basin flow field prediction 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 Boltzmann equation and corresponding macro control equation and constructing multi-scale macro flux, the simulation efficiency of cross-basin flow problems is improved while maintaining the simulation accuracy.

[0075] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through 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 easily understood from the description of the embodiments in conjunction with the following drawings, in which:

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

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

[0079] Figure 3 : The 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) rotation temperature cloud map;

[0082] Figure 6 :The distribution of pressure coefficient and heat flux coefficient on the surface 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 symmetric surface of the X-38 aircraft surface; (a) pressure coefficient distribution, (b) heat flux coefficient distribution. DETAILED DESCRIPTION

[0084] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not 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 the cross-basin flow of near-space aircraft, in which the calculation of interface flux in red font and the Boltzmann equation and the corresponding macroscopic adjoint equation in the red box are the key technologies of the present invention. The specific steps of the cross-basin flow field simulation method include:

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

[0087] Step 2: Set the flow field variables at the initial moment. In this embodiment, according to 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 to describe the distribution of gas particles in the phase space, which represents the number density of particles with a specific speed at a certain time and position.

[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 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 calculated using macroscopic quantities (such as density, momentum, energy, etc.), represents the relaxation time calculated based on the interface macroscopic quantity, 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 In order to facilitate the calculation of h ij The temporary variable defined, CFL phys The CFL number that satisfies the stability condition is set, 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 can be decomposed into balanced flux and unbalanced flux, namely

[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 spatial differential of velocity, T t is the translational temperature, as well as Represents the pressure at the interface ij near 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 the 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 its 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 is a certain error between them). To pass The calculated equilibrium distribution function set.

[0102] Combining equations (1)-(6), we can obtain the macro flux applicable to the entire basin, and the calculation amount is greatly simplified. The distribution function flux can be directly obtained by spatial reconstruction to obtain the distribution function of the unit interface and then simply calculated. It can be seen that the largest amount of calculation in the current method of calculating interface flux lies in spatial reconstruction, which is greatly simplified compared to UGKS and DUGKS.

[0103] If the explicit method is used to solve the Boltzmann equation, the problem of "small time advancement step and low computational efficiency" cannot be solved, so the fully implicit method is used in the present invention to solve it. 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 equal sign of the Boltzmann equation. Because this term represents the collision of particles, it is called the "right-hand collision term" here. The equilibrium distribution function is related to the macroscopic quantity, and the macroscopic quantity is obtained by numerical integration of the distribution function in the discrete velocity method. Therefore, there is a strong coupling effect between the two. If accurate solution is to be obtained, the amount of calculation involved is huge. For this reason, in the present invention, the estimated macroscopic quantity is first obtained by implicitly solving the corresponding macroscopic adjoint equation, and then the equilibrium distribution function corresponding to the estimated macroscopic quantity is brought into the right-hand term in the Boltzmann equation, which can greatly simplify 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 solving the entire algorithm. In addition, since the discrete velocity method has a huge demand for computational memory, in order to save memory requirements, point relaxation symmetric Gauss-Seidel iteration is used when implicitly solving the control equation to reduce the additional memory consumption caused by implicit solution. The calculation diagram of this process is shown in the figure. 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 macro 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 unlimited 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=0.74 is usually set.

[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 unit 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:

[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 quantities of unit i at time n+1.

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

[0125] The implicit governing equation for solving 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 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 cell i. The calculation formula is

[0128]

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

[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 numbered k at time n+1.

[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 converges. If converged, execute step 8; if not, return to step 3. Generally, the velocity second 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 iteration steps away from the reference iteration step, and ε is the convergence threshold. Assuming that the current iteration step is step, and the reference iteration step is set to be n iteration steps away from the current iteration step, the reference iteration step is step-n, and n is a manually set value, which is set to 100 in this embodiment.

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

[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 pressure coefficient and heat flux coefficient distribution on the symmetric surface of the X-38 aircraft are shown, and compared with the simulation results of the classic algorithm DSMC. The results show that the simulation results of the current algorithm are in good agreement with the simulation results of the DSMC method. Table 1 shows the lift coefficient and drag coefficient calculated by the current method and the DSMC method. The results show that the error between the current method and the DSMC method is within 5%. Table 2 shows the computing resources consumed by the current method and the DSMC method to simulate the current working conditions on the same computing platform. From the results, it can be seen that the computing efficiency of the current method has obvious advantages.

[0146] Table 1 Comparison of lift and drag coefficients of 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 is to be understood that the above embodiments are exemplary 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 combined with 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 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 interface macroscopic quantity, h ij Represents local time steps; Step 4: Using the macro flux obtained in step 3, implicitly solve the macro adjoint equation to obtain the estimated macro quantity; Step 5: Using the estimated macroscopic quantity obtained in step 4 and the distribution function flux obtained in step 3, the Boltzmann equation is implicitly solved to obtain the distribution function of 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. An efficient numerical method for simulating near-space aircraft 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 is a temporary variable, CFL phys is the number of CFLs that meet the stability conditions.

3. The efficient numerical method for simulating near-space aircraft 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 particle, is the particle's velocity, is the rotational speed of the particle, is the spatial differential of velocity, 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 the macroscopic quantity of the interface The corresponding equilibrium distribution function, f i is the set of distribution functions of the center of unit i, is the set of equilibrium distribution functions at 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 aircraft cross-basin flow according to claim 1, characterized in that: The process of implicitly solving 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 macro 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 quantities of unit i at time n+1.

5. An efficient numerical method for simulating near-space aircraft 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 aircraft 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 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 numbered k at time n+1.

7. An efficient numerical method for simulating near-space aircraft 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 aircraft cross-basin flow according to claim 1, characterized in that: Step 6 The process of updating the flow field variables using the distribution function is: 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 aircraft cross-basin flow according to claim 1, characterized in that: Step 7 uses the velocity second norm error as the convergence criterion, and the criterion formula is: in represents the velocity field of the reference iteration step, It represents the velocity field n iterations away from the reference iteration, and ε is the convergence threshold.

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