直接模拟蒙特卡罗方法(Direct Simulation Monte Carlo,DSMC)已经广泛用于稀薄空气动力学计算模拟,而直接数值求解Boltzmann方程目前还只局限于简单流动,比如一维线性问题.高度非线性、积分微分属性的Boltzmann方程的求解关键是碰撞积...直接模拟蒙特卡罗方法(Direct Simulation Monte Carlo,DSMC)已经广泛用于稀薄空气动力学计算模拟,而直接数值求解Boltzmann方程目前还只局限于简单流动,比如一维线性问题.高度非线性、积分微分属性的Boltzmann方程的求解关键是碰撞积分建模问题.最近,快速谱方法的提出和完善,使得对复杂的三维非线性问题直接求解Boltzmann方程带来了希望.相对于DSMC,快速谱方法具有数值上确定性的优势,在低速多尺度流动计算模拟上更为高效.本文介绍了快速谱方法在求解气体动理学方程的最新发展和成果,并探讨其应用前景.快速谱方法的推广应用使之真正成为DSMC的补充方法,现在面临的困难是需要发展新的气体动理学模型来描述多原子、多组分、稠密气体等.本文最后介绍了这方面的最新进展和直接求解Boltzmann模型方程气体动理论统一算法在模拟计算跨流域气体绕流及航天再入高超声速气动问题的应用.展开更多
A newly discovered Ballistic Principle of the Property Balance in the Space (BPPBS) occupied by the gas is introduced to simplify and reduce computations in applications dealing with modeling of fluid dynamics problem...A newly discovered Ballistic Principle of the Property Balance in the Space (BPPBS) occupied by the gas is introduced to simplify and reduce computations in applications dealing with modeling of fluid dynamics problems. The integro-differential balance equations for mass, momentum, and energy, which were formulated by applying the BPPBS, are derived. The integro-differential balance equations for mass and momentum were further approximated for the collision-dominated flow regime. Then they were reduced to the corresponding vector differential equations by the method of vector differentiation with subsequent elimination of the terms belonging to the original equation. It was shown that in the collision-dominated flow regime, the derived vector differential equations of mass and momentum balance are identical to the corresponding Navier-Stokes equations. This finding validates the BPPBS and suggests that, in the collision-dominated flow regime, the formulated integro-differential forms of the balance are exact implicit solutions for corresponding Navier-Stokes equations. Six additional tests demonstrating the feasibility of the proposed method and validity of the BPPBS are presented here. The BPPBS and the methodology discussed here will be highly useful not only as the basis to solve the fluid dynamics problems, but also to model any dynamic system composed of presumably chaotically moving particles/elements, each carrying a specific amount of property/information.展开更多
The low-variance direct simulation Monte Carlo(LVDSMC)is a powerful method to simulate low-speed rarefied gas flows.However,in the near-continuum flow regime,due to limitations on the time step and spatial cell size,i...The low-variance direct simulation Monte Carlo(LVDSMC)is a powerful method to simulate low-speed rarefied gas flows.However,in the near-continuum flow regime,due to limitations on the time step and spatial cell size,it takes plenty of time to find the steady-state solution.Here we remove these deficiencies by coupling the LVDSMC with the general synthetic iterative scheme(GSIS)which permits the simulation at the hydrodynamic scale rather than the much smaller kinetic scale.As a proof of concept,we propose the stochastic-deterministic coupling method based on the Bhatnagar-Gross-Krook kinetic model.First,macroscopic synthetic equations are derived exactly from the kinetic equation,which not only contain the Navier-Stokes-Fourier constitutive relation,but also encompass the higher-order terms describing the rarefaction effects.Then,the high-order terms are extracted from LVDSMC and fed into synthetic equations to predict the macroscopic properties which are closer to the steady-state solution than LVDSMC.Finally,the state of simulation particles in LVDSMC is updated to reflect the change of macroscopic properties.As a result,the convergence to steady state is greatly accelerated,and the restrictions on cell size and the time step are removed.We conduct the Fourier stability analysis and simulate several canonical rarefied gas flows to demonstrate the advantages of LVDSMC-GSIS:when the Knudsen number is lower than 0.1,it can use the grid size about 10 times larger than that in traditional DSMC,and it can reduce the computational cost by two orders of magnitude in the flow regime.展开更多
The DSMC modeling is developed to simulate three-dimensional(3D)rarefied ionization flows and numerically forecast the communication blackout around spacecraft during hypervelocity reentry.A new weighting factor schem...The DSMC modeling is developed to simulate three-dimensional(3D)rarefied ionization flows and numerically forecast the communication blackout around spacecraft during hypervelocity reentry.A new weighting factor scheme for rare species is introduced,whose key point is to modify the corresponding chemical reaction coefficients involving electrons,meanwhile reproduce the rare species in resultants and preserve/delete common species in reactants according to the weighting factors.The resulting DSMC method is highly efficient in simulating weakly inhomogeneous flows including the Couette shear flow and controlling statistical fluctuation with high resolution.The accurate reliability of the present DSMC modeling is also validated by the comparison with a series of experimental measurements of the Shenzhou reentry capsule tested in a low-density wind tunnel from the HAI of CARDC.The obtained electron number density distribution for the RAM-C II vehicle agrees well with the flight experiment data,while the electron density contours for the Stardust hypervelocity reentry match the reference data completely.In addition,the present 3D DSMC algorithm can capture distribution of the electron,N+and O+number densities better than the axis-symmetric DSMC model.The introduction of rare species weighting factor scheme can significantly improve the smoothness of the number density contours of rare species,especially for that of electron in weak ionization case,while it has negligible effect on the macroscopic flow parameters.The ionization characteristics of the Chinese lunar capsule reentry process are numerically analyzed and forecasted in the rarefied transitional flow regime at the flying altitudes between 80 and 97 km,and the simulations predict communication blackout altitudes which are in good agreement with the actual reentry flight data.For the spacecraft reentry with hypervelocity larger than the second cosmic speed,it is forecasted and verified by the present DSMC modeling that ionization reactions will cover the windwa展开更多
The purpose of this work is to describe the suitable methods for aerodynamic characteristics calculation of hypersonic vehicles in free molecular flow and the transitional regimes. Moving of the hypersonic vehicles at...The purpose of this work is to describe the suitable methods for aerodynamic characteristics calculation of hypersonic vehicles in free molecular flow and the transitional regimes. Moving of the hypersonic vehicles at high altitude, it is necessary to know the behavior of its aerodynamic characteristics for all flow regimes. Nowadays, various engineering approaches have been developed for modelling of aerodynamics of aircraft vehicle designs at initial state. The engineering method that described in this paper provides good results for the aerodynamic characteristics of various geometry designs of hypersonic vehicles in the transitional regime. In this paper present the calculation results of aerodynamic characteristics of various hypersonic vehicles in all range of regimes by using engineering method.展开更多
文摘直接模拟蒙特卡罗方法(Direct Simulation Monte Carlo,DSMC)已经广泛用于稀薄空气动力学计算模拟,而直接数值求解Boltzmann方程目前还只局限于简单流动,比如一维线性问题.高度非线性、积分微分属性的Boltzmann方程的求解关键是碰撞积分建模问题.最近,快速谱方法的提出和完善,使得对复杂的三维非线性问题直接求解Boltzmann方程带来了希望.相对于DSMC,快速谱方法具有数值上确定性的优势,在低速多尺度流动计算模拟上更为高效.本文介绍了快速谱方法在求解气体动理学方程的最新发展和成果,并探讨其应用前景.快速谱方法的推广应用使之真正成为DSMC的补充方法,现在面临的困难是需要发展新的气体动理学模型来描述多原子、多组分、稠密气体等.本文最后介绍了这方面的最新进展和直接求解Boltzmann模型方程气体动理论统一算法在模拟计算跨流域气体绕流及航天再入高超声速气动问题的应用.
文摘A newly discovered Ballistic Principle of the Property Balance in the Space (BPPBS) occupied by the gas is introduced to simplify and reduce computations in applications dealing with modeling of fluid dynamics problems. The integro-differential balance equations for mass, momentum, and energy, which were formulated by applying the BPPBS, are derived. The integro-differential balance equations for mass and momentum were further approximated for the collision-dominated flow regime. Then they were reduced to the corresponding vector differential equations by the method of vector differentiation with subsequent elimination of the terms belonging to the original equation. It was shown that in the collision-dominated flow regime, the derived vector differential equations of mass and momentum balance are identical to the corresponding Navier-Stokes equations. This finding validates the BPPBS and suggests that, in the collision-dominated flow regime, the formulated integro-differential forms of the balance are exact implicit solutions for corresponding Navier-Stokes equations. Six additional tests demonstrating the feasibility of the proposed method and validity of the BPPBS are presented here. The BPPBS and the methodology discussed here will be highly useful not only as the basis to solve the fluid dynamics problems, but also to model any dynamic system composed of presumably chaotically moving particles/elements, each carrying a specific amount of property/information.
基金the National Natural Science Foundation of China under the grant No. 12172162.
文摘The low-variance direct simulation Monte Carlo(LVDSMC)is a powerful method to simulate low-speed rarefied gas flows.However,in the near-continuum flow regime,due to limitations on the time step and spatial cell size,it takes plenty of time to find the steady-state solution.Here we remove these deficiencies by coupling the LVDSMC with the general synthetic iterative scheme(GSIS)which permits the simulation at the hydrodynamic scale rather than the much smaller kinetic scale.As a proof of concept,we propose the stochastic-deterministic coupling method based on the Bhatnagar-Gross-Krook kinetic model.First,macroscopic synthetic equations are derived exactly from the kinetic equation,which not only contain the Navier-Stokes-Fourier constitutive relation,but also encompass the higher-order terms describing the rarefaction effects.Then,the high-order terms are extracted from LVDSMC and fed into synthetic equations to predict the macroscopic properties which are closer to the steady-state solution than LVDSMC.Finally,the state of simulation particles in LVDSMC is updated to reflect the change of macroscopic properties.As a result,the convergence to steady state is greatly accelerated,and the restrictions on cell size and the time step are removed.We conduct the Fourier stability analysis and simulate several canonical rarefied gas flows to demonstrate the advantages of LVDSMC-GSIS:when the Knudsen number is lower than 0.1,it can use the grid size about 10 times larger than that in traditional DSMC,and it can reduce the computational cost by two orders of magnitude in the flow regime.
基金the National Natural Science Foundation(Nos.11602288&91530319)the National Key Basic Research and Development Program(2014CB744100)the National Outstanding Youth Fund(11325212)of China,and the UK Royal Academy of Engineering for Distinguished Visiting Fellowships(DVF1516/3/57).
文摘The DSMC modeling is developed to simulate three-dimensional(3D)rarefied ionization flows and numerically forecast the communication blackout around spacecraft during hypervelocity reentry.A new weighting factor scheme for rare species is introduced,whose key point is to modify the corresponding chemical reaction coefficients involving electrons,meanwhile reproduce the rare species in resultants and preserve/delete common species in reactants according to the weighting factors.The resulting DSMC method is highly efficient in simulating weakly inhomogeneous flows including the Couette shear flow and controlling statistical fluctuation with high resolution.The accurate reliability of the present DSMC modeling is also validated by the comparison with a series of experimental measurements of the Shenzhou reentry capsule tested in a low-density wind tunnel from the HAI of CARDC.The obtained electron number density distribution for the RAM-C II vehicle agrees well with the flight experiment data,while the electron density contours for the Stardust hypervelocity reentry match the reference data completely.In addition,the present 3D DSMC algorithm can capture distribution of the electron,N+and O+number densities better than the axis-symmetric DSMC model.The introduction of rare species weighting factor scheme can significantly improve the smoothness of the number density contours of rare species,especially for that of electron in weak ionization case,while it has negligible effect on the macroscopic flow parameters.The ionization characteristics of the Chinese lunar capsule reentry process are numerically analyzed and forecasted in the rarefied transitional flow regime at the flying altitudes between 80 and 97 km,and the simulations predict communication blackout altitudes which are in good agreement with the actual reentry flight data.For the spacecraft reentry with hypervelocity larger than the second cosmic speed,it is forecasted and verified by the present DSMC modeling that ionization reactions will cover the windwa
文摘The purpose of this work is to describe the suitable methods for aerodynamic characteristics calculation of hypersonic vehicles in free molecular flow and the transitional regimes. Moving of the hypersonic vehicles at high altitude, it is necessary to know the behavior of its aerodynamic characteristics for all flow regimes. Nowadays, various engineering approaches have been developed for modelling of aerodynamics of aircraft vehicle designs at initial state. The engineering method that described in this paper provides good results for the aerodynamic characteristics of various geometry designs of hypersonic vehicles in the transitional regime. In this paper present the calculation results of aerodynamic characteristics of various hypersonic vehicles in all range of regimes by using engineering method.
