Discrete speed improving method for rotation unbalance calculation of diatomic molecules

Abstract

The invention discloses an improved discrete velocity method for rotation unbalance calculation of diatomic molecules, and relates to the field of numerical simulation of rarefied gas dynamics. The method comprises the steps that a flow field is initialized according to actual working conditions, a Boltzmann equation based on a Rykov model is adopted as a control equation, a collision-free Boltzmann equation is solved to obtain a unit interface distribution function, a macroscopic equation flux corresponding to a local solution of the collision-free Boltzmann equation and a macroscopic equation flux corresponding to a Navier-Stokes equation considering the molecular rotation effect are calculated, and a unit interface distribution function is obtained; performing weighted calculation on the two types of fluxes according to the rarefaction degree of the gas to obtain a macroscopic flux, solving a macroscopic adjoint equation to obtain an estimated macroscopic quantity and an estimated equilibrium state distribution function, solving a microcosmic control equation to update the distribution function, and integrating the distribution function to update the macroscopic quantity and judge the convergence. On the basis of keeping the conciseness of the traditional semi-implicit discrete velocity method, the method can achieve the precise prediction of the full-basin unbalanced flow field of the diatomic molecular gas.

Description

Technical Field

[0001] The present invention relates to the field of numerical simulation of rarefied gas dynamics, and more particularly to an improved discrete velocity method for nonequilibrium calculation of diatomic molecule rotation. Background Art

[0002] The phenomenon of non-equilibrium flow across multiple flow basins is widely present in aerospace engineering, such as: hypersonic near-space vehicles, return capsules, aircraft engines, etc. Due to the thin atmosphere in near-space, aircraft can fly at a large Mach number, which has become a strategic focus for all countries. However, when the aircraft flies at high speed, the gas around the windward area such as the leading edge is highly compressed, the molecular mean free path is small, the collision frequency is high, and it shows the characteristics of a continuous flow basin. In areas such as the trailing edge, the gas is in a highly rarefied state due to the "vacuum" effect. Near-space vehicles are difficult to study because of the highly non-equilibrium and unstable flow field around them and because they span multiple flow basins. At present, due to the difficulty and high cost of experiments, numerical simulation methods are mainly used to study such problems.

[0003] Traditional macroscopic methods, such as the Euler equation or the Navier-Stokes equation, use the continuity assumption and assume that the flow field is always in equilibrium. They ignore the non-equilibrium effects caused by gas discontinuity and are completely unsuitable for numerical simulation of rarefied flow problems.

[0004] The Boltzmann equation, derived from the kinetic theory of gases, describes the evolution of the distribution function of gas molecules over time. Compared with the Navier-Stokes equation, it is free from the limitation of the continuous medium assumption. Therefore, the Boltzmann equation is theoretically capable of describing flow problems from continuous flow to rarefied flow.

[0005] Solving the Boltzmann equation requires integration in the particle's velocity space. During simulation, the particle velocity space is usually truncated to a certain area and discretized into a finite number of velocity integration points. The resulting control equation is usually called the discrete velocity Boltzmann equation (DVBE), and the numerical method for solving DVBE is usually called the discrete velocity method (DVM).

[0006] In the traditional discrete velocity method, in order to obtain better stability, the collision term of the Boltzmann equation is usually discretized in a semi-implicit format, that is, the macroscopic quantity at the current moment is used to estimate the equilibrium distribution function at the next moment, and it is used to calculate the collision term. At the same time, this method ignores the collision effect of particles at the unit interface, which makes the grid size of its physical space need to be smaller than the mean free path of particle collision to ensure the accuracy of the calculation results. Therefore, this method has low computational efficiency and poor accuracy in continuous flow and near-continuous flow domains where particle collisions are frequent.

[0007] The improved discrete velocity method achieves accurate prediction of the equilibrium state by introducing the macroscopic adjoint equation, thereby realizing the fully implicit discretization of the collision term of the Boltzmann equation, and considering the collision effect of particles when calculating the macroscopic flux of the unit interface, solving the problem that the grid scale is limited by the molecular mean free path, and has high accuracy and computational efficiency in the simulation of the whole flow domain. However, this method currently only realizes the numerical simulation of the gas flow problem of single atomic molecules, and has not yet realized the numerical simulation of the gas flow of diatomic molecules. In actual engineering applications, the air, which is the main research object, has its main components oxygen and nitrogen, both of which are diatomic molecules. In addition, the rotational excitation temperatures of oxygen and nitrogen are 2.08K and 2.07K, respectively, which indicates that when performing numerical simulations, the rotational freedom of molecules should be taken into account under most working conditions. Especially in the thermal non-equilibrium flow problem containing shock waves, the translational temperature and rotational temperature of some areas in the flow field are not equal, and should not be expressed by the same temperature. Therefore, it is urgent to develop an improved discrete velocity method that can consider the rotational freedom of molecules to achieve a more realistic numerical simulation of the gas flow problem in the whole flow domain. Summary of the invention

[0008] To solve the above problems, the present invention provides an improved discrete velocity method for nonequilibrium calculation of diatomic molecule rotation.

[0009] The technical solution adopted by the present invention includes:

[0010] (1) Initialize the flow field according to the actual working conditions to obtain the initial equilibrium distribution function, and use it as the initial distribution function;

[0011] (2) Calculate the distribution function f i n , macroscopic conservation quantity The spatial derivative of .

[0012] (3) From the local solution of the collisionless Boltzmann equation, according to the distribution function f i n and its spatial derivative to calculate the unit interface distribution function

[0013] (4) According to the unit interface distribution function Calculating the Macroscopic Flux Corresponding to the Local Solution of the Collisionless Boltzmann Equation

[0014] (5) Calculate the macro equation flux corresponding to the Navier-Stokes equation considering the molecular rotation effect

[0015] (6) Solve the macroscopic adjoint equation, and according to the macroscopic equation flux corresponding to the local solution of the collisionless Boltzmann equation The macro equation flux corresponding to the Navier-Stokes equation considering the molecular rotation effect Calculate the estimated macroscopic conservation And calculate the estimated equilibrium distribution function

[0016] (7) Solve the Boltzmann-Rykov equation and use the estimated equilibrium distribution function and the unit interface distribution function Update the distribution function f i n+1 ;

[0017] (8) Update the macroscopic quantities and judge the convergence. If it does not converge, repeat the above steps from step (2) until the convergence conditions are met to obtain the macroscopic quantities and distribution functions of the flow field.

[0018] The improved discrete velocity method for calculating the nonequilibrium effect of diatomic molecular rotation adopts the Boltzmann-Rykov equation to simultaneously consider the translation and rotation of the molecule. The Boltzmann-Rykov equation is expressed as follows:

[0019]

[0020]

[0021] In the formula, f represents the distribution function, f * represents the equilibrium distribution function, f t and f r They represent the equilibrium distribution function of translation and rotation respectively, ξ represents the particle velocity, Z represents the number of rotational collisions (i.e., the ratio of the relaxation rates of elastic collisions and inelastic collisions of particles), t represents time, and τ represents the collision time.

[0022] The macroscopic conservation quantities include gas density ρ, momentum per unit volume of gas ρu, total energy per unit volume of gas ρE and rotational energy per unit volume of gas ρE rThe macroscopic conservation quantities and stress P, translational heat flow q t and the rotational heat flux q r The calculation formula is as follows:

[0023]

[0024] P = ∫ccfdΕ;

[0025]

[0026]

[0027] In the formula, W represents the macroscopic conservation quantity, P represents stress, u represents the macroscopic velocity, c=ξ-u represents the thermal motion velocity of the molecule, ζ represents the rotation velocity of the molecule, and dΕ=dξdζ represents the integral differential element in the velocity space. The heat flow q is the sum of the translational heat flow and the rotational heat flow, that is, q=q t +q r . is the microscopic moment vector, that is

[0028] The unit interface distribution function ignores the collision effect and is calculated using the upwind format. The expression is as follows:

[0029]

[0030] In the formula, represents the unit interface distribution function, and represents the distribution function on the left and right sides of the unit interface, n ij represents the unit external normal vector of element i at its interface with element j, x ij is the center coordinate of the interface between unit i and unit j. The distribution functions on the left and right sides of the unit interface are obtained by interpolating the unit center distribution function using limiters.

[0031] The macroscopic adjoint equation is obtained by momenting the Boltzmann-Rykov equation in the particle velocity space, and the expression is as follows:

[0032]

[0033]

[0034] Where F represents the macroscopic flux, and S represents the source term generated after the introduction of rotational freedom.

[0035] The flux of the macroscopic adjoint equation is obtained by solving the Boltzmann-Rykov equation locally at the unit interface, and the expression is as follows:

[0036]

[0037]

[0038] In the formula, F c and F v denote the inviscid flux and viscous flux respectively, F DVM represents the macroscopic equation flux contributed by the local solution of the collisionless Boltzmann equation, F NS It represents the macro equation flux contributed by the Navier-Stokes equation considering the molecular rotation effect. p is the local physical time step, determined by the CFL condition.

[0039] The macro equation flux contributed by the local solution of the collisionless Boltzmann equation is calculated by the unit interface distribution function without considering molecular collisions. Find the moment in the particle velocity space.

[0040] The macro equation flux contributed by the Navier-Stokes equation considering the molecular rotation effect is directly calculated from the macro quantity.

[0041] The microscopic control equation, i.e. the fully implicitly discretized Boltzmann-Rykov equation, is expressed as follows:

[0042]

[0043] In the formula, subscript i represents unit i, subscript ij represents the interface between unit i and unit j, superscript n and n+1 represent the time step, j∈N(i) represents the unit around unit i, V i represents the volume of unit i, n ij represents the unit external normal vector of unit i on the interface with unit j, S ij represents the interface area between unit i and unit j, represents the equilibrium distribution function of unit i at time n+1 estimated by the macroscopic adjoint equation, Represents the distribution function on the interface between unit i and unit j at time n+1.

[0044] Preferably, the equation can be solved using flux splitting and the LU-SGS (Lower-Upper Symmetric Gauss-Seidel) implicit method.

[0045] The macroscopic adjoint equation is discretized using the finite volume method, and the discretized expression is as follows:

[0046]

[0047] In the formula, Represents the increment of macroscopic conserved quantity.

[0048] The inviscid flux can be directly calculated by the traditional CFD flux format, preferably the lattice Boltzmann flux algorithm (LBFS). The viscous flux is obtained by central difference, and the source term is calculated based on the physical quantity at the center of the unit.

[0049] Optionally, the LU-SGS implicit algorithm can be used to speed up the convergence when solving the macroscopic control equations.

[0050] Compared with the prior art, the present invention has at least the following effects: (1) Compared with the improved discrete velocity method for monatomic gas molecules, the present invention takes into account the rotational non-equilibrium effect of diatomic molecules during simulation, which is closer to the real atmospheric conditions and can better simulate thermal non-equilibrium flow problems. (2) It overcomes the defects of the traditional semi-implicit discrete velocity method, while keeping the calculation simple, it improves the solution accuracy and efficiency in continuous flow and near-continuous flow domains. (3) Compared with the traditional semi-implicit discrete velocity method, by solving the macroscopic adjoint equation to predict the equilibrium state, the collision term is fully implicitly discretized, which accelerates the convergence speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 1 is a schematic diagram of the steps of an improved discrete velocity method for calculating the non-equilibrium effect of diatomic molecule rotation provided by an embodiment of the present invention;

[0052] Figure 2 It is a distribution curve diagram of equilibrium temperature and rotation temperature of a shock tube at t=0.2s under different Knudsen numbers provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0053] The following specifically explains the implementation mode of the present invention in conjunction with the accompanying drawings. The examples are provided only for illustrative purposes and should not be construed as limitations of the present invention. All other embodiments obtained by ordinary technicians in the field without creative work based on the examples in the present invention are within the scope of protection of the present invention.

[0054] The present invention provides an improved discrete velocity method for nonequilibrium calculation of diatomic molecular rotation, such as Figure 1 As shown, the method comprises the following steps:

[0055] (1) Initialize the flow field according to the actual working conditions to obtain the initial equilibrium distribution function, and use it as the initial distribution function;

[0056] The improved discrete velocity method suitable for calculating the non-equilibrium effect of diatomic molecular rotation provided in the embodiment of the present invention gives an initial flow field according to actual working conditions, calculates the equilibrium distribution function according to the macroscopic quantity of the initial flow field, and uses the equilibrium distribution function as the initial value of the distribution function.

[0057] Optionally, for complex flow problems, the results obtained by solving the macro equations can be used for initialization.

[0058] Among them, the microscopic control equation, namely the Boltzmann-Rykov equation, is expressed as follows:

[0059]

[0060]

[0061] In the formula, f represents the distribution function, f * represents the equilibrium distribution function, f t and f r They represent the equilibrium distribution functions of translation and rotation respectively, ξ represents the particle velocity, Z represents the number of rotational collisions (i.e., the ratio of the relaxation rates of elastic collisions and inelastic collisions of particles), t represents time, and τ represents the collision time.

[0062] The equilibrium distribution function of the translation and the equilibrium distribution function of the rotation are expressed as follows:

[0063]

[0064]

[0065] In the formula, ρ represents density, K represents the number of rotational degrees of freedom, u represents macroscopic velocity, c = ξ-u represents the thermal motion velocity of molecules, ζ represents the rotation velocity of molecules, and q t and q r represent translational heat flow and rotational heat flow respectively. The heat flow q is the sum of the translational heat flow and the rotational heat flow, that is, q = q t +q r ,λ t , r and λ eq Respectively with the translation temperature T t , rotation temperature T r and equilibrium temperature T eq Related to λ t,r,eq =1 / 2RT t,r,eq , σ, ω0 and ω1 are relevant parameters in the model and are related to the gas properties.

[0066] (2) Calculate the distribution function f i n , macroscopic conservation quantity The spatial derivative of .

[0067] The distribution function f i n , macroscopic conservation quantity The spatial derivative of is calculated based on the distribution function of the adjacent unit centers, the macroscopic conservation quantity and the coordinates.

[0068] (3) From the local solution of the collisionless Boltzmann equation, according to the distribution function f i n and its spatial derivative to calculate the unit interface distribution function

[0069] The unit interface distribution function ignores molecular collisions and is calculated using the upwind format. The expression is as follows:

[0070]

[0071] In the formula, represents the unit interface distribution function, and represents the distribution function on the left and right sides of the unit interface, n ij represents the unit external normal vector of element i at its interface with element j, x ij is the center coordinate of the interface between unit i and unit j. The distribution functions on the left and right sides of the unit interface can be obtained by interpolating the unit center distribution function using a limiter, and the limiter can be selected according to requirements.

[0072] (4) According to the unit interface distribution function Calculating the Macroscopic Flux Corresponding to the Local Solution of the Collisionless Boltzmann Equation

[0073] The macroscopic equation flux corresponding to the local solution of the collisionless Boltzmann equation is By considering the unit interface distribution function without considering molecular collision The moment is obtained in the velocity space, and the calculation formula is as follows:

[0074]

[0075] Wherein, dΕ=dξdζ represents the integral differential element in velocity space.

[0076] (5) Calculate the macro equation flux corresponding to the Navier-Stokes equation considering the molecular rotation effect

[0077] The macro equation flux corresponding to the Navier-Stokes equation considering the molecular rotation effect According to the calculation of the macroscopic adjoint equation considering the rotation effect, the macroscopic adjoint equation and the viscous flux F v , inviscid flux F c , the expression of the source term S is as follows:

[0078]

[0079] F NS =F c +F v ;

[0080] F c =[ρu,ρuu+pI,(ρE+p)u,ρE r u] T ;

[0081]

[0082]

[0083]

[0084] In the formula, W represents the macroscopic conservation quantity, ρu represents the momentum of gas per unit volume, ρE represents the total energy of gas per unit volume, and ρE r Represents the rotational energy per unit volume of gas, E r,eq represents the rotational energy at equilibrium, p represents the pressure, R represents the gas molecular constant, and I represents the unit tensor. represents the viscous stress tensor, They represent heat flux, translational heat flux and rotational heat flux respectively, and the expressions are as follows:

[0085]

[0086]

[0087]

[0088]

[0089] In the formula, μ represents the viscosity coefficient, and its magnitude is only related to the translation temperature. Its expression is as follows:

[0090]

[0091] Where, T ref and μ ref denote the reference temperature and the reference viscosity coefficient respectively, and ω denotes the coefficient related to the intermolecular collision model.

[0092] (6) Solve the macroscopic adjoint equation, and according to the macroscopic equation flux corresponding to the local solution of the collisionless Boltzmann equation The macro equation flux corresponding to the Navier-Stokes equation considering the molecular rotation effect Calculate the estimated macroscopic conservation And calculate the estimated equilibrium distribution function

[0093] The macroscopic adjoint equation is spatially discretized using the finite volume method, and the expression is as follows:

[0094]

[0095]

[0096]

[0097] In the formula, represents the increment of the macroscopic conservation quantity, j∈N(i) represents the unit around unit i, represents the macroscopic flux at the unit interface, V i represents the volume of unit i, S ij Represents the area of ​​the interface between unit i and unit j. Δt p is the local physical time step, determined by the CFL condition.

[0098] The inviscid flux of the macroscopic adjoint equation is directly calculated by the traditional CFD equation flux format, preferably the lattice Boltzmann flux algorithm (LBFS). The viscous flux is obtained by central difference, and the source term is calculated by the physical quantity at the cell center.

[0099] Optionally, the LU-SGS implicit method can be used to solve the macroscopic adjoint equation to speed up the convergence.

[0100] The estimated equilibrium distribution function of the new time Using estimated macroscopic conservation quantities It is calculated using the equilibrium distribution function expression in step (1).

[0101] (7) Solve the Boltzmann-Rykov equation and use the estimated equilibrium distribution function and the unit interface distribution function Update distribution function

[0102] The microscopic control equation is expressed as follows:

[0103]

[0104] Introducing Increment The above equation can be rewritten as:

[0105]

[0106]

[0107] Preferably, the equation can be solved using the LU-SGS implicit method to simplify the calculation. The expression is as follows:

[0108]

[0109]

[0110]

[0111] Among them, D i and D j The expression is as follows:

[0112]

[0113]

[0114] (8) Update the macroscopic quantities and judge the convergence. If it does not converge, repeat the above steps from step (2) until the convergence conditions are met to obtain the macroscopic quantities and distribution functions of the flow field.

[0115] The macroscopic conservation quantities, as well as the expressions for stress, translational heat flow and rotational heat flow are as follows:

[0116]

[0117] P = ∫ccfdΕ;

[0118]

[0119]

[0120] Where P represents stress, represents the microscopic moment vector, that is Total energy per unit volume ρE and rotational energy per unit volume ρE r The expression is as follows:

[0121]

[0122]

[0123] Compare the updated macro-conservation quantity with the macro-conservation quantity of the previous step to determine whether it converges. If so, stop the iteration; otherwise, return to step (2) to continue the iteration.

[0124] In order to facilitate understanding of the improved discrete velocity method for calculating the non-equilibrium effect of diatomic molecule rotation proposed in the embodiment of the present invention, and to verify the accuracy and full-domain characteristics of the present invention, this embodiment is analyzed and explained in detail through the following examples.

[0125] The one-dimensional nitrogen shock tube is a classic example for verifying the ability of numerical simulation methods to handle complex non-equilibrium flow problems. It has high requirements on the stability, accuracy, and computational efficiency of the numerical simulation method, and there are multiple reference solutions. It is an excellent example for verifying the effectiveness of this embodiment in simulating flow problems containing non-equilibrium effects of diatomic molecular rotation.

[0126] This example first sets the initial working condition, and the physical field settings are as follows:

[0127] Different Knudsen numbers Kn=0.001, 0.01, 0.1, 1, the rotational collision number is Z=2.4, and the global CFL number is 0.8. The physical space is x∈[0,1], uniformly discretized into 200 grid units, and the initial values ​​of each macroscopic physical quantity are as follows:

[0128]

[0129] The velocity space is [-10, 10], which is evenly discretized into 201 velocity points, and the Newton-Cotes integral is used to calculate its weight.

[0130] In this example, the hard sphere model is used to calculate the gas viscosity coefficient (ω = 1), and the local molecular collision time and reference viscosity coefficient are expressed as follows:

[0131]

[0132]

[0133] In the formula, ρ ref represents the reference density, L represents the characteristic length, and Kn represents the Knudsen number. The reference temperature is taken as T ref =1.

[0134] Figure 2 The distribution curves of equilibrium temperature and rotation temperature at t = 0.2s are shown for different Knudsen numbers. Figure 2 It can be seen that with the increase of the Knudsen number, the rarefaction effect is enhanced, and the gap between the equilibrium temperature and the rotational temperature is gradually widened, indicating that the rotational non-equilibrium effect is also enhanced; the calculation results of the current algorithm are in good agreement with the results of the unified gas kinetic scheme (UGKS) and the multi-scale discrete velocity method (MDVM) used as reference solutions, which verifies that the present invention has the ability to simulate the flow containing the rotational non-equilibrium effect of diatomic molecules in the entire flow domain.

[0135] The above-mentioned embodiments only express several preferred implementation modes of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention, and these improvements and substitutions should also be regarded as the protection scope of this application. Therefore, the protection scope of the patent of this application shall be based on the protection scope of the claims.

Claims

1. An improved discrete velocity method for non-equilibrium calculation of diatomic molecular rotation, in which the Boltzmann-Rykov equation is used as the control equation and the corresponding equilibrium distribution function is used to consider the rotation of molecules and better simulate real gas; the macro equation flux is divided into two parts: the macro equation flux corresponding to the local solution of the collisionless Boltzmann equation and the macro equation flux corresponding to the Navier-Stokes equation considering the molecular rotation effect, so as to consider the collision effect of the unit interface and improve the accuracy and efficiency in the continuous and near-continuous flow domains; the local solution of the collisionless Boltzmann equation is used to obtain the unit interface distribution function; the Navier-Stokes equation considering the molecular rotation effect is used to obtain the corresponding macro equation flux; the macro quantity is updated by integrating the moment of the distribution function. The specific steps are as follows: (1) Initialize the flow field according to the actual working conditions to obtain the initial equilibrium distribution function, and use it as the initial distribution function; (2) Calculate the distribution function f i n , macroscopic conservation quantity The spatial derivative of (3) From the local solution of the collisionless Boltzmann equation, according to the distribution function f i n and its spatial derivative to calculate the unit interface distribution function (4) According to the unit interface distribution function Calculating the Macroscopic Flux Corresponding to the Local Solution of the Collisionless Boltzmann Equation (5) Calculate the macro equation flux corresponding to the Navier-Stokes equation considering the molecular rotation effect (6) Solve the macroscopic adjoint equation, and according to the macroscopic equation flux corresponding to the local solution of the collisionless Boltzmann equation The macro equation flux corresponding to the Navier-Stokes equation considering the molecular rotation effect Calculate the estimated macroscopic conservation And calculate the estimated equilibrium distribution function (7) Solve the Boltzmann-Rykov equation and use the estimated equilibrium distribution function and the unit interface distribution function Update the distribution function f i n+1 ; (8) Update the macroscopic quantities and judge the convergence. If it does not converge, repeat the above steps from step (2) until the convergence conditions are met to obtain the macroscopic quantities and distribution functions of the flow field.

2. An improved discrete velocity method for rotational nonequilibrium calculation of diatomic molecules as claimed in claim 1, characterized in that: The microscopic control equation adopts the Boltzmann-Rykov equation, which is expressed as follows: In the formula, f represents the distribution function, f * represents the equilibrium distribution function, f t and f r They represent the equilibrium distribution function of translation and rotation respectively, ξ represents the particle velocity, Z represents the number of rotational collisions, that is, the ratio of the relaxation rates of elastic collisions and inelastic collisions of particles, t represents time, and τ represents the particle collision time.

3. An improved discrete velocity method for rotational nonequilibrium calculation of diatomic molecules as claimed in claim 1, characterized in that: The macroscopic conserved quantities include gas density, momentum per unit volume of gas, total energy and rotational energy per unit volume of gas. The expressions for calculating the fluid density, momentum, total energy and rotational energy using the distribution function are: Where W represents the macroscopic conservation quantity, ρ represents the gas density, u represents the macroscopic velocity, ρE and ρE r are the total energy and rotational energy of the gas per unit volume, respectively, dΕ=dξdζ represents the integral differential element in the velocity space; is the microscopic moment vector, that is where ζ is the rotation speed of the molecule.

4. An improved discrete velocity method for rotational nonequilibrium calculation of diatomic molecules as claimed in claim 1, characterized in that: The evolution equation of its updated distribution function is: Where, subscript i represents unit i, subscript ij represents the interface between units i and j, superscript n and n+1 represent the time step, V i represents the volume of unit i, j∈N(i) represents the unit around unit i, n ij represents the unit external normal vector of unit i on the interface with unit j, S ij represents the area of ​​the interface between unit i and unit j, represents the equilibrium distribution function of unit i at time n+1 estimated by the macroscopic adjoint equation, represents the distribution function on the interface between unit i and unit j at time n+1; Introducing Increment The distribution function evolution equation can be rewritten as:

5. An improved discrete velocity method for rotational nonequilibrium calculation of diatomic molecules as claimed in claim 1, characterized in that: The expression of the interface flux F is as follows: In the formula, Δt p is the local physical time step, determined by the CFL condition. DVM represents the macroscopic equation flux contributed by the local solution of the collisionless Boltzmann equation, F NS represents the macro equation flux contributed by the Navier-Stokes equation considering the molecular rotation effect, F c and F v denote the inviscid flux and viscous flux respectively, Represents the unit interface distribution function when particle collisions are not considered.

6. An improved discrete velocity method for rotational nonequilibrium calculation of diatomic molecules as claimed in claim 1, characterized in that: The Navier-Stokes equation considering the molecular rotation effect is as follows: F NS =F c +F v ; F c =[ρu,ρuu+pI,(ρE+p)u,ρE r u] T ; In the formula, W represents the macroscopic variable, S represents the source term, p represents the pressure, I represents the unit tensor, and E r,eq represents the rotational energy at equilibrium, R represents the gas molecule constant, represents the viscous stress tensor, They represent heat flux, translational heat flux and rotational heat flux respectively, K represents the rotational degree of freedom, T eq represents the equilibrium temperature.

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