A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of ...A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.展开更多
In rarefied gas flows,the spatial grid size could vary by several orders of magnitude in a single flow configuration(e.g.,inside the Knudsen layer it is at the order of mean free path of gas molecules,while in the bul...In rarefied gas flows,the spatial grid size could vary by several orders of magnitude in a single flow configuration(e.g.,inside the Knudsen layer it is at the order of mean free path of gas molecules,while in the bulk region it is at a much larger hydrodynamic scale).Therefore,efficient implicit numerical method is urgently needed for time-dependent problems.However,the integro-differential nature of gas kinetic equations poses a grand challenge,as the gain part of the collision operator is non-invertible.Hence an iterative solver is required in each time step,which usually takes a lot of iterations in the(near)continuum flow regime where the Knudsen number is small;worse still,the solution does not asymptotically preserve the fluid dynamic limit when the spatial cell size is not refined enough.Based on the general synthetic iteration scheme for steady-state solution of the Boltzmann equation,we propose two numerical schemes to push the multiscale simulation of unsteady rarefied gas flows to a new boundary,that is,the numerical solution not only converges within dozens of iterations in each time step,but also asymptotically preserves the Navier-Stokes-Fourier limit in the continuum flow regime,when the spatial grid is coarse,and the time step is large(e.g.,in simulating the extreme slow decay of two-dimensional Taylor vortex,the time step is even at the order of vortex decay time).The properties of fast convergence and asymptotic preserving of the proposed schemes are not only rigorously proven by the Fourier stability analysis for simplified gas kinetic models,but also demonstrated by several numerical examples for the gas kinetic models and the Boltzmann equation.展开更多
On June 25, 2016, the Long March 7(LM-7) launch vehicle completed its maiden flight successfully. LM-7, as a new generation of medium and basic launch vehicle based on the design concepts of non-toxic and nonpolluting...On June 25, 2016, the Long March 7(LM-7) launch vehicle completed its maiden flight successfully. LM-7, as a new generation of medium and basic launch vehicle based on the design concepts of non-toxic and nonpolluting, was developed for the purpose of launching a cargo spacecraft to the Chinese space station. Based on the experience on launching cargo spacecraft and satellites, LM-7 can be adapted for mainstream satellite launch missions in the future with its characteristics of serialization and continuous optimization. LM-7 is expected to be used to launch manned spacecraft in the future. This paper presents a general review of LM-7 with regard to the general scheme and provides references for the development prospects of a medium launch vehicle series in China.展开更多
The heat conduction under fast external excitation exists in many experiments measuring the thermal conductivity in solids,which is described by the phonon Boltzmann equation,i.e.,the Callaway’s model with dual relax...The heat conduction under fast external excitation exists in many experiments measuring the thermal conductivity in solids,which is described by the phonon Boltzmann equation,i.e.,the Callaway’s model with dual relaxation times.Such a kinetic system has two spatial Knudsen numbers related to the resistive and normal scatterings,and one temporal Knudsen number determined by the external oscillation frequency.Thus,it is a challenge to develop an efficient numerical method.Here we first propose the general synthetic iterative scheme(GSIS)to solve the phonon Boltzmann equation,with the fast-converging and asymptotic-preserving properties:(i)the solution can be found within dozens of iterations for a wide range of Knudsen numbers and frequencies,and(ii)the solution is accurate when the spatial cell size in the bulk region is much larger than the phonon mean free path.Then,we investigate how the heating frequency affects the heat conduction in different transport regimes.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
基金The Project Supported by National Natural Science Foundation of China.
文摘A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.
基金supported by the National Natural Science Foundation of China(12172162)the Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications in China(2020B1212030001).
文摘In rarefied gas flows,the spatial grid size could vary by several orders of magnitude in a single flow configuration(e.g.,inside the Knudsen layer it is at the order of mean free path of gas molecules,while in the bulk region it is at a much larger hydrodynamic scale).Therefore,efficient implicit numerical method is urgently needed for time-dependent problems.However,the integro-differential nature of gas kinetic equations poses a grand challenge,as the gain part of the collision operator is non-invertible.Hence an iterative solver is required in each time step,which usually takes a lot of iterations in the(near)continuum flow regime where the Knudsen number is small;worse still,the solution does not asymptotically preserve the fluid dynamic limit when the spatial cell size is not refined enough.Based on the general synthetic iteration scheme for steady-state solution of the Boltzmann equation,we propose two numerical schemes to push the multiscale simulation of unsteady rarefied gas flows to a new boundary,that is,the numerical solution not only converges within dozens of iterations in each time step,but also asymptotically preserves the Navier-Stokes-Fourier limit in the continuum flow regime,when the spatial grid is coarse,and the time step is large(e.g.,in simulating the extreme slow decay of two-dimensional Taylor vortex,the time step is even at the order of vortex decay time).The properties of fast convergence and asymptotic preserving of the proposed schemes are not only rigorously proven by the Fourier stability analysis for simplified gas kinetic models,but also demonstrated by several numerical examples for the gas kinetic models and the Boltzmann equation.
文摘On June 25, 2016, the Long March 7(LM-7) launch vehicle completed its maiden flight successfully. LM-7, as a new generation of medium and basic launch vehicle based on the design concepts of non-toxic and nonpolluting, was developed for the purpose of launching a cargo spacecraft to the Chinese space station. Based on the experience on launching cargo spacecraft and satellites, LM-7 can be adapted for mainstream satellite launch missions in the future with its characteristics of serialization and continuous optimization. LM-7 is expected to be used to launch manned spacecraft in the future. This paper presents a general review of LM-7 with regard to the general scheme and provides references for the development prospects of a medium launch vehicle series in China.
文摘The heat conduction under fast external excitation exists in many experiments measuring the thermal conductivity in solids,which is described by the phonon Boltzmann equation,i.e.,the Callaway’s model with dual relaxation times.Such a kinetic system has two spatial Knudsen numbers related to the resistive and normal scatterings,and one temporal Knudsen number determined by the external oscillation frequency.Thus,it is a challenge to develop an efficient numerical method.Here we first propose the general synthetic iterative scheme(GSIS)to solve the phonon Boltzmann equation,with the fast-converging and asymptotic-preserving properties:(i)the solution can be found within dozens of iterations for a wide range of Knudsen numbers and frequencies,and(ii)the solution is accurate when the spatial cell size in the bulk region is much larger than the phonon mean free path.Then,we investigate how the heating frequency affects the heat conduction in different transport regimes.
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.
