The strategy of information exchange in N-S / DSMC coupling algorithm by using Bayesian estimation method

Abstract

The application discloses a strategy for information exchange in an N-S / DSMC coupling algorithm by using a Bayesian estimation method, and comprises the following steps: in the information exchange between a DSMC calculation region based on the Bayesian estimation method and an N-S solving region, the moving temperature T tr , the rotating temperature T rot , the vibration temperature T vib and the density of the velocity gas are estimated by using DSMC statistical samples, and the estimated values are taken as the results of the DSMC and are used for information exchange with the N-S calculation. The application provides a strategy for information exchange in an N-S / DSMC coupling algorithm by using a Bayesian estimation method, can give better parameter estimation under the condition of less DSMC sampling sample amount while ensuring the consistency of the calculation results and the precision, provides the N-S solving, and effectively improves the information exchange efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft aerodynamics, and involves the numerical simulation of the aerodynamic heating characteristics of hypersonic flow around an aircraft. Aiming at the implementation of information exchange between two calculation methods in the N-S / DSMC coupling algorithm in the transitional flow region of the aircraft, it specifically relates to a strategy for information exchange in the N-S / DSMC coupling algorithm using the Bayesian estimation method. Background Art

[0002] When studying the aerodynamic characteristics of the flow around an aircraft, generally, according to the numerical range of Kn (Knudsen number) (i.e., the ratio of the mean free path of gas molecules to the flow characteristic length), the flow problems experienced by the spacecraft are roughly divided into: continuum flow region (Kn < 10 -3 ), transitional flow region (10 -3 < Kn < 10), free molecular flow region (Kn > 10). Among them, the aerodynamic problems in the transitional flow region are the most complex. This flow region can be further divided into near continuum flow, slip flow, and rarefied transitional flow. The flow in the transitional region between the continuum flow and the free molecular flow is a kind of flow that is difficult to handle in numerical calculations. In order to study the aerodynamic characteristics of an aircraft across various flow fields, the traditional approach is to use a set of algorithms for rarefied flow, such as the DSMC (Direct Simulation Monte Carlo) method; and for continuum flow, there is a set of research methods, such as numerically solving the Euler, N-S (Navier-Stokes) equations, etc.; the two types of methods are quite different, independent of each other, and it is difficult for the calculation results to be smoothly connected with height.

[0003] In the transitional flow region, the N-S / DSMC coupling algorithm is a solution approach. In a flow field, the flow field is divided into a continuum flow region and a region where the continuum flow equation fails. The N-S equation is used to solve the continuum flow region, and the DSMC method is used in the region where the continuum flow equation fails, which can expand the application scope of the N-S equation and the DSMC method and improve the calculation efficiency of the DSMC method.

[0004] During the process of coupling calculation between the two methods, information exchange is required. When the N-S solution region provides boundary information to the DSMC solution region, it is relatively simple, and the parameters of each simulation molecule entering the DSMC region are sampled according to the local parameters. However, when DSMC provides boundary conditions for N-S, due to the large statistical fluctuations in the instantaneous results of DSMC, it will affect the stability of the N-S solution process, and in severe cases, it will cause the solution to diverge and cannot continue.

[0005] In the prior art, the generally adopted "under-relaxation" technology is used to achieve it. Its coupling calculation structure can meet the test requirements, but its disadvantage is that the efficiency of information exchange is too low, affecting the calculation process. Summary of the Invention

[0006] One object of the present invention is to solve at least the above-mentioned problems and / or defects, and to provide at least the advantages described below.

[0007] To achieve these objectives and other advantages of the present invention, a strategy for information exchange in the NS / DSMC coupled algorithm using a Bayesian estimation method is provided. The process for information exchange between the NS solution region and the DSMC computation region based on the Bayesian estimation method is configured to include:

[0008] S1. Using DSMC statistical molecular velocity samples, and employing a normal-inverse gamma conjugate prior distribution, the velocity calculated in the previous step of NS and the migration temperature are used as priors to estimate the velocity. and the temperature of gas movement T tr ;

[0009] S2. Using DSMC to statistically analyze rotational and vibrational energy samples, and employing a normal-inverse gamma conjugate prior distribution, the rotational and vibrational temperature values ​​calculated in the previous step (NS) are used as priors to estimate the rotational temperature T. rot Vibration temperature T vib ;

[0010] S3. Using the DSMC statistical density sample, and employing the normal conjugate prior distribution, estimate the density by taking the density value calculated in the previous step of NS as the prior.

[0011] S4. Exchange information between the estimates obtained in S41-S43 and the NS calculation as the results of DSMC.

[0012] Preferably, in S1, the speed and the temperature of gas movement T tr The estimation process includes:

[0013] Taking the x-direction as an example, the overall velocity distribution of the molecules can be written as a conventional normal distribution as follows:

[0014]

[0015] Where R is the gas constant, T trx Let θ be the temperature shift in the x-direction, σ be the estimated mean, and σ be the mean temperature shift in the 2 Let be the variance, and u be the molecular velocity in the x-direction. Let be the average molecular velocity in the x-direction;

[0016] Given n velocity samples X(x1, ..., xn) of a certain gas composition, n By estimating the mean θ and variance σ 2 Thus obtain T tr ;

[0017] θ, σ 2 The prior distribution adopts the following normal-inverse gamma conjugate prior distribution:

[0018]

[0019] Where k0 and υ0 are hyperparameters that need to be determined through debugging in AI; θ0, These are the prior mean and variance;

[0020] (θ,σ 2 The joint posterior density function is:

[0021]

[0022] in,

[0023] v n =n+υ0

[0024] k n =n+k0

[0025]

[0026]

[0027] Where n is the sample size; k0 is determined through debugging. Then, we can obtain v n k n θ n υ n ;

[0028] θ, σ 2 The corresponding maximum posterior probability Bayesian estimation They are respectively:

[0029]

[0030]

[0031] in, The sample mean is:

[0032]

[0033] S 2 For the sample variance:

[0034]

[0035] The velocity u calculated by NS N-S and temperature T trN-S Obtain the prior mean and variance θ0.

[0036] 90 = u N-S

[0037]

[0038] By analyzing θ and σ 2 From the estimation, we can obtain the x-direction. and moving temperature T trx :

[0039]

[0040]

[0041] Using the same method, Bayesian estimation is performed in the y and z directions to obtain the velocity in the y direction. and temperature T try velocity in the z direction and temperature T trz Then the temperature of the gas movement T tr for:

[0042]

[0043] k0 and v0 are used as hyperparameters. Through debugging, parameter settings suitable for hypersonic flow can be provided.

[0044] Preferably, in S2, the rotational temperature T rot The estimation process includes:

[0045] The rotational energy can be expressed as a regular gamma distribution as follows:

[0046]

[0047] Where Γ(r) is the gamma function, λ and r are the parameters in the gamma function, and ζ rot Let k be the rotational degree of freedom, k be the Boltzmann constant, and ε be the vibrational energy.

[0048] The conjugate prior distribution of λ is Γ(α, β).

[0049]

[0050] Where α and β are the parameters in the gamma function;

[0051] For n rotational energy samples X(x1, ..., x) in the gas component n ), λ-maximum a posteriori probability Bayesian estimation for:

[0052]

[0053] in:

[0054]

[0055]

[0056] Where A is the undetermined hyperparameter, T rotN-S The rotational temperature is calculated using NS.

[0057] Then the rotation temperature T rot Obtained through the following formula:

[0058]

[0059] The vibration temperature T vib The estimation method is related to the rotation temperature T rot The estimation method is configured to be consistent.

[0060] Preferably, in S3, the density estimation process is configured to include:

[0061] The density can be expressed as a regular normal distribution as follows:

[0062]

[0063] Based on n density samples X(x1, ... x) of gas components n Estimate the mean θ to obtain the density mean.

[0064] Using the same conjugate prior distribution and Bayesian estimation as in S41, Based on the following formula:

[0065]

[0066] Where θ0 is the density value ρ calculated by NS. N-S The obtained prior mean,

[0067] θ0=ρ N-S

[0068] k0 is used as a hyperparameter. Through debugging, parameter settings suitable for hypersonic flow are provided. Here, the value of k0 is related to...

[0069] Preferably, before exchanging information between the DSMC computation domain using the Bayesian estimation method and the NS solution domain, the method further includes:

[0070] Step 1: Solve the NS equations for chemical nonequilibrium flow in the continuous flow region and perform chemical nonequilibrium DSMC calculations based on rarefied flow.

[0071] Step 2: Solve for the local Knudsen number based on the NS equation calculation results, and divide the flow field into continuous flow region and rarefied flow region based on the DSMC calculation results to obtain the corresponding boundary surface;

[0072] Step 1: Calculate the non-equilibrium distribution on the boundary surface based on the calculation results of the NS equation, and sample the non-equilibrium distribution into the DSMC calculation region to simulate molecular parameters, providing boundary conditions for DSMC calculation.

[0073] The present invention has at least the following beneficial effects:

[0074] In order to suppress the impact of DSMC statistical fluctuations on the NS solution process, this invention adopts an artificial intelligence Bayesian estimation algorithm to replace the "sub-relaxation" technique generally used in the prior art. It can provide better parameter estimates for NS solution with a smaller DSMC sampling sample size while ensuring the consistency of calculation results and accuracy, thus effectively improving the efficiency of information exchange.

[0075] (1) The present invention adopts a conjugate prior distribution, which avoids a large amount of computation in Bayesian estimation during the information exchange process from DSMC to NS.

[0076] (2) The present invention uses the previous result of NS calculation as the prior value, which facilitates the prior requirements in the Bayesian estimation process.

[0077] (3) The present invention adopts a unified grid system, which facilitates the automatic partitioning judgment and information exchange calculation in the calculation process.

[0078] (4) The present invention uses automatic partitioning technology to determine which regions are in the region where the continuous flow equation fails during the calculation process, which has strong adaptability.

[0079] (4) The present invention adopts a non-equilibrium boundary and considers the influence of non-equilibrium effect during the information exchange process from NS to DSMC.

[0080] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0081] Figure 1 This is a flowchart of the NS / DSMC coupled calculation process in this invention;

[0082] Figure 2 This is a schematic diagram of automatic partitioning in this invention;

[0083] Figure 3 This is a schematic diagram of the partitioning determination in this invention;

[0084] Figure 4 This is a schematic diagram of the interface judgment of the present invention;

[0085] Figure 5 This is a schematic diagram showing a curve comparison between the present invention and the prior art. Detailed Implementation

[0086] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0087] To mitigate the impact of DSMC statistical fluctuations on the NS solution process, this invention employs an artificial intelligence Bayesian estimation algorithm to replace the commonly used "sub-relaxation" technique. The Bayesian algorithm, based on Bayes' theorem, is an artificial intelligence algorithm and a type of estimation method based on posterior probability distributions, which incorporate prior and sample information. Its basic idea is to treat the parameter to be estimated θ as a random variable with a prior probability density l(θ), and based on the sample set X, give the posterior probability distribution π(θ|X). Based on the posterior probability distribution, estimate the optimal value of θ. Using the Bayesian estimation method, a better parameter estimate is provided for the NS solution with a smaller DSMC sampling sample size.

[0088] Example:

[0089] An information exchange technique for artificial intelligence Bayesian methods applicable to NS / DSMC coupling algorithms, such as Figure 1 The process includes:

[0090] Step 1: Calculations based on solving the Navier-Stokes equations in the continuous flow region and DSMC calculations based on rarefied flows, including:

[0091] S11. Numerical calculations of the Neumann equations (NS) in continuous flow regions were performed. The governing equations were the (thermo)chemical nonequilibrium NS equations. The Gordon and McBride fitting formulas were used to calculate gas thermodynamic properties, the Gupta and Yos viscosity coefficient fitting formulas, the Eucken relation, and the Wike mixing rule were used to calculate gas transport properties, and the Dunn & Kang chemical kinetic model and the Millikan and White vibrational relaxation formulas were used to calculate thermochemical source terms. The grid system was the same as that used in the DSMC. Numerical discretization of the governing equations employed methods such as the confined volume method, Steger-Warming splitting, the NND scheme, and the DPLUR implicit scheme. In each iteration step, the NS equations exchanged information with the DSMC after obtaining flow field data such as component mass fractions, velocity, temperature, and pressure.

[0092] S12. Calculations were performed using the DSMC method in the rarefied flow region. The variable stiff sphere molecular model (VHS) and the Larsen-Borgnakke collision model were used to calculate energy transfer during molecular collisions. The same chemical reaction model used in the NS calculations was employed to calculate the five-component thermochemical nonequilibrium process of air. A three-temperature model (moving temperature, rotational temperature, and vibrational temperature) was used, with the moving and rotational temperatures averaged by degrees of freedom and then used as a single temperature for information exchange with the NS calculations. A two-dimensional Cartesian mesh system was used: the surface mesh A (or facet mesh) was a triangular unstructured mesh; the spatial background mesh B (or spatial mesh) was an equidistant Cartesian mesh (e.g., ...). Figure 2 The collision subgrid is adaptive according to the flow field density, and the selection of collision pairs is restricted to the collision subgrid.

[0093] Step 2: Automatic partitioning based on the local Knudsen number, which includes:

[0094] S21. Calculate the local Knudsen number based on the NS calculation results. The local Knudsen number represents the degree of scarcity within a specific grid in the flow field.

[0095]

[0096] Where: λ is the mean free path of gas molecules in the local flow field; Q is the macroscopic parameter of the local flow field, which can be pressure, density or temperature.

[0097] S22. Scan each grid cell to determine which partition it belongs to. Calculate the local Knudsen number using temperature, pressure, and temperature respectively. Calculate Kn using the flow parameter with the largest gradient. l When Kn l A value ≥0.02 indicates that the continuous flow equations have failed, and the DSMC method is used to simulate this grid. During the calculation, the computational domain of the DSMC method is continuously adjusted based on the NS calculation results until the flow field reaches a stable state. Figure 3 In the middle, C is the NS area, D is the interface, and E is the DSMC area.

[0098] S23. Determine the boundary surface. Scan each grid cell and its surrounding grid cells. If a grid cell is a DSMC computational grid, and its adjacent grid cell is a non-DSMC grid, then the interface between these two grid cells is the boundary surface (i.e., ...). Figure 4 (at point F).

[0099] Step 3: Information exchange between the NS solution domain and the DSMC computation domain based on the local weakly non-equilibrium state.

[0100] S31. Using the results calculated by NS, calculate the non-equilibrium distribution on the boundary. According to the continuous flow failure judgment method, when K nlWhen the velocity distribution is ≥0.02, non-equilibrium phenomena begin to appear at the coupled boundary. At this time, the velocity distribution function no longer conforms to the Maxwell equilibrium distribution and can be described by the Chapman-Enskog distribution.

[0101] For a non-equilibrium distribution that deviates from the Maxwell distribution, its first-order expansion is:

[0102] f(C)=f0(C)Γ(C)

[0103] Where C is the dimensionless molecular thermal velocity.

[0104] C = c / (2kT / m) 1 / 2

[0105] Where c is the molecular thermal velocity, k is the Boltzmann constant, T is the gas temperature, and m is the gas molecule mass.

[0106]

[0107]

[0108]

[0109]

[0110] Among them, C x,y,z Let τ be the dimensionless molecular thermal velocity in the x, y, and z directions, τ be the shear stress, q be the heat flux, κ be the thermal conductivity coefficient, p be the pressure, and μ be the viscosity coefficient.

[0111] S32. Determine the molecular parameters for simulation within the DSMC computational domain based on the non-equilibrium distribution. Provide molecular velocities conforming to the Chapman-Enskog distribution at the boundary surface. Using a velocity sampling method based on the Maxwell distribution, and considering the local non-equilibrium, generate molecular velocities conforming to the Chapman-Enskog distribution through a random "reject-accept" step. The steps are as follows:

[0112] (1) Calculate the local τ based on the results of the Navier-Stokes equations. i,j and q i ,Pick

[0113] B≡max(|τ i,j |,|q i |)

[0114] (2) Set amplitude parameters

[0115] A = 1 + 30B

[0116] (3) Generate a velocity vector C based on the Maxwell distribution. try .

[0117] (4) Generate a random number R f ,if

[0118] AR f ≤Γ(C)

[0119] Accept C try Otherwise, return to (3) to generate a new C. try .

[0120] (5) Give the molecular velocity

[0121] c = (2kT / m) 1 / 2 c try +u

[0122] Where u is the macroscopic velocity component on the boundary surface.

[0123] Step 4: Information exchange between the DSMC computational domain and the NS solution domain based on Bayesian estimation. This includes:

[0124] S41. Using DSMC statistical molecular velocity samples, and employing a normal-inverse gamma conjugate prior distribution, the velocity calculated in the previous step of NS and the migration temperature are used as priors to estimate the velocity. and moving temperature T tr .

[0125] Taking the x-direction as an example, the overall velocity distribution of the molecules follows a normal distribution:

[0126]

[0127] Where u is the molecular velocity in the x-direction. Let R be the average molecular velocity in the x-direction, R be the gas constant, and T be the average molecular velocity in the x-direction. trx The temperature moves in the x-direction.

[0128] Represented as a regular normal distribution:

[0129]

[0130] Given n velocity samples X(x1, ..., xn) of a certain gas component n Estimate the mean θ and variance σ. 2 Thus obtain T tr .

[0131] θ, σ 2 The prior distribution adopts a conjugate prior distribution: normal-inverse gamma distribution.

[0132]

[0133] Where k0 and υ0 are hyperparameters that need to be determined through debugging in AI; θ0, These are the prior mean and variance;

[0134] (θ,σ 2 The joint posterior density function is

[0135]

[0136] in,

[0137] v n =n+υ0

[0138] k n =n+k0

[0139]

[0140]

[0141] (θ,σ 2 The maximum a posteriori probability Bayesian estimate is:

[0142]

[0143]

[0144] Among them, the sample mean

[0145]

[0146] Sample variance

[0147]

[0148] The velocity u calculated by NS N-S and temperature T trN-S Obtain the prior mean and variance θ0.

[0149] θ0=u N-S

[0150]

[0151] By analyzing θ and σ 2 From the estimation, we can obtain the x-direction. and moving temperature T trx :

[0152]

[0153]

[0154] The same Bayesian estimation method is used for other directions (y, z) to obtain the velocity in the y direction. and temperature T try velocity in the z direction and temperature T trz .

[0155] Gas movement temperature T tr for

[0156]

[0157] k0 and υ0 are used as hyperparameters, and through debugging, parameter settings suitable for hypersonic flow can be provided.

[0158] S42. Using DSMC to statistically analyze rotational energy samples, and employing the gamma conjugate prior distribution, estimate the rotational temperature T using the rotational temperature calculated in the previous step of NS as the prior. rot .

[0159] The rotational energy distribution follows a gamma distribution.

[0160]

[0161] Where ε is the rotational energy, ζ rot For rotational degree of freedom, T rot This refers to the rotational temperature.

[0162] Written as a regular gamma distribution

[0163]

[0164] The conjugate prior distribution of λ is Γ(α, β).

[0165]

[0166] Given n rotational energy samples X(x1, ..., xn) of a certain gas component n )

[0167] Therefore, the Bayesian estimate of the maximum a posteriori probability of λ is:

[0168]

[0169] in:

[0170]

[0171]

[0172] Where A is a hyperparameter, and through adjustment, parameter settings suitable for hypersonic flow are provided. T rotN-SThe rotational temperature is calculated using NS.

[0173] Rotation temperature can be obtained

[0174]

[0175] S43. Using DSMC to statistically analyze vibration energy samples, and employing the gamma conjugate prior distribution, the vibration temperature calculated in the previous step of NS is used as the prior to estimate the vibration temperature T. vib .

[0176] The distribution of vibrational energy is completely identical to that of rotational energy, satisfying the gamma distribution.

[0177]

[0178] Where ε is the vibrational energy, ζ vib For the vibrational degrees of freedom, T vib The vibration temperature.

[0179] Since the distribution of vibrational energy is exactly the same as that of rotational energy, the same Bayesian estimation method can be used. Given n vibrational energy samples X(x1, ..., xn) of a certain gas component... n )

[0180] Therefore, the Bayesian estimate of the maximum a posteriori probability of λ is:

[0181]

[0182] in:

[0183]

[0184]

[0185] Where A is a hyperparameter, and through adjustment, parameter settings suitable for hypersonic flow are provided. T vibN-S The rotational temperature is calculated using NS. Vibrational degrees of freedom are expressed via T. vibN-S Find out,

[0186]

[0187] Where, θ vib The vibration characteristic temperature is the main component.

[0188] S44. Using the DSMC statistical density sample, and employing the normal conjugate prior distribution, estimate the density by taking the density calculated in the previous step of NS as the prior.

[0189] Assume the density follows a normal distribution.

[0190]

[0191] Represented as a regular normal distribution:

[0192]

[0193] Given n density samples X(x1, ..., xn) of a certain gas component n Estimate the mean θ, and thus obtain

[0194] Using the same conjugate prior distribution and Bayesian estimation as in S41, we can obtain

[0195]

[0196] Among them, the density ρ calculated by NS N-S The prior mean θ0 is obtained.

[0197] θ o =P N-S

[0198] k0 is used as a hyperparameter. Through debugging, a parameter setting suitable for hypersonic flow can be provided. Here, the value of k0 is different from the value in S41.

[0199] S45. Exchange information between the above estimates as the results of DSMC and NS calculation.

[0200] like Figure 5 As shown, the Bayesian estimation algorithm of this scheme replaces the "sub-relaxation" technique generally used. The effect is that, in the process of temperature change from 300K to 1300K, Bayesian estimation can reach the target temperature in about 30 steps, while sub-relaxation requires 80 steps to reach the target temperature, thus improving the efficiency of information exchange.

[0201] The above solution is merely an illustration of a preferred example and is not limited thereto. When implementing this invention, appropriate substitutions and / or modifications can be made according to the user's needs.

[0202] The number of devices and processing scale described herein are for the purpose of simplifying the description of the invention. Applications, modifications, and variations of the invention will be readily apparent to those skilled in the art.

[0203] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Other modifications can be readily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and examples shown and described herein.

Claims

1. A strategy for information exchange in the NS / DSMC coupled algorithm using Bayesian estimation, characterized in that, The process for exchanging information between the NS solution domain and the DSMC computation domain based on the Bayesian estimation method is configured to include: S1. Using DSMC statistical molecular velocity samples, and employing a normal-inverse gamma conjugate prior distribution, the velocity calculated in the previous step of NS and the migration temperature are used as priors to estimate the velocity. and the moving temperature of the gas ; S2. Using DSMC to statistically analyze rotational and vibrational energy samples, and employing a normal-inverse gamma conjugate prior distribution, the rotational and vibrational temperature values ​​calculated in the previous step of NS are used as priors to estimate the rotational temperature. Vibration temperature ; S3. Using the DSMC statistical density sample, and employing the normal conjugate prior distribution, estimate the density by taking the density value calculated in the previous step of NS as the prior. S4. Exchange information between the estimates obtained in S1-S3 and the NS calculation, using the results of DSMC.

2. The strategy for information exchange in the NS / DSMC coupled algorithm using Bayesian estimation method as described in claim 1, characterized in that, In S1, the speed and the moving temperature of the gas The estimation process includes: Taking the x-direction as an example, the overall velocity distribution of the molecules can be written as a conventional normal distribution as follows: Where R is the gas constant. Temperature shifted in the x-direction. To estimate the mean, For variance, Let x be the molecular velocity in the x-direction. Let be the average molecular velocity in the x-direction; Given a certain gas component n A velocity sample X ( x 1 , …x n ), by estimating the mean and variance Thus obtain , ; , The prior distribution adopts the following normal-inverse gamma conjugate prior distribution: in, , These are hyperparameters that need to be determined through debugging; , These are the prior mean and variance; The joint posterior density function is: in, Where n is the sample size; determined through debugging. , After that, we can obtain , , , ; , The corresponding maximum posterior probability Bayesian estimation , They are respectively: Among them, the sample mean : Sample variance : Speed ​​calculated by NS and temperature Obtain the prior mean and variance , : Through the , From the estimation, we can obtain the x-direction. and moving temperature : Using the same method, Bayesian estimation is performed in the y and z directions to obtain the velocity in the y direction. and temperature velocity in the z direction and temperature Then the temperature at which the gas moves for: , As a hyperparameter, through tuning, parameter settings suitable for hypersonic flow are provided.

3. The strategy for information exchange in the NS / DSMC coupled algorithm using Bayesian estimation method as described in claim 1, characterized in that, In S2, the rotational temperature The estimation process includes: The rotational energy can be expressed as a regular gamma distribution as follows: in, For gamma function, r are the parameters in the gamma function. Let k be the rotational degree of freedom, and k be the Boltzmann constant. It is rotational energy; The conjugate prior distribution is : in, α , β These are the parameters in the gamma function; For gas components n A rotational energy sample X ( x 1 , …x n ), Maximum a posteriori probability Bayesian estimation for: in: in, A These are undetermined hyperparameters. The rotational temperature is calculated using NS. Then rotation temperature Obtained through the following formula: The vibration temperature The estimation method and rotation temperature The estimation method is configured to be consistent.

4. The strategy for information exchange in the NS / DSMC coupled algorithm using Bayesian estimation method as described in claim 1, characterized in that, In S3, the density estimation process is configured to include: The density can be expressed as a regular normal distribution as follows: Based on gas components n density samples X ( x 1 , …x n ), estimated mean Thus, the average density is obtained. ; Using the same conjugate prior distribution and Bayesian estimation as in S1, Based on the following formula: in, Density calculated using NS The obtained prior mean, in, These are hyperparameters to be determined.

5. The strategy for information exchange in the NS / DSMC coupled algorithm using Bayesian estimation method as described in claim 1, characterized in that, Before the DSMC computational domain using the Bayesian estimation method exchanges information with the NS solution domain, it also includes: Step 1: Solve the NS equations for chemical nonequilibrium flow in the continuous flow region and perform chemical nonequilibrium DSMC calculations based on rarefied flow. Step 2: Solve for the local Knudsen number based on the NS equation calculation results, and divide the flow field into continuous flow region and rarefied flow region based on the DSMC calculation results to obtain the corresponding boundary surface; Step 3: Calculate the non-equilibrium distribution on the boundary surface based on the calculation results of the NS equation, and sample the molecular parameters into the DSMC calculation region according to the non-equilibrium distribution to provide boundary conditions for DSMC calculation.

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