A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows Ⅱ:Multi-Dimensional Cases  

作　　者：Juan-Chen Huang Kun Xu Pubing Yu 

机构地区：[1]Department of Merchant Marine,Taiwan Ocean University,Keelung 20224,Taiwan [2]Department of Mathematics,Hong Kong University of Science and Technology,Clear Water Bay,Kowloon,Hong Kong

出　　处：《Communications in Computational Physics》2012年第8期662-690,共29页计算物理通讯（英文）

基　　金：supported by Hong Kong Research Grant Council 621709 and 621011,National Natural Science Foundation of China(Project No.10928205);National Key Basic Research Program(2009CB724101);J.C.Huang was supported by National Science Council of Taiwan through grant no.NSC 100-2221-E-019-048-MY3。

摘　　要：With discretized particle velocity space,a multi-scale unified gas-kinetic scheme for entire Knudsen number flows has been constructed based on the kinetic model in one-dimensional case[J.Comput.Phys.,vol.229(2010),pp.7747-7764].For the kinetic equation,to extend a one-dimensional scheme to multidimensional flow is not so straightforward.The major factor is that addition of one dimension in physical space causes the distribution function to become two-dimensional,rather than axially symmetric,in velocity space.In this paper,a unified gas-kinetic scheme based on the Shakhov model in two-dimensional space will be presented.Instead of particle-based modeling for the rarefied flow,such as the direct simulation Monte Carlo(DSMC)method,the philosophical principal underlying the current study is a partial-differential-equation(PDE)-based modeling.Since the valid scale of the kinetic equation and the scale of mesh size and time step may be significantly different,the gas evolution in a discretized space is modeled with the help of kinetic equation,instead of directly solving the partial differential equation.Due to the use of both hydrodynamic and kinetic scales flow physics in a gas evolution model at the cell interface,the unified scheme can basically present accurate solution in all flow regimes from the free molecule to the Navier-Stokes solutions.In comparison with the DSMC and Navier-Stokes flow solvers,the current method is much more efficient than DSMC in low speed transition and continuum flow regimes,and it has better capability than NS solver in capturing of non-equilibrium flow physics in the transition and rarefied flow regimes.As a result,the current method can be useful in the flow simulation where both continuum and rarefied flow physics needs to be resolved in a single computation.This paper will extensively evaluate the performance of the unified scheme fromfreemolecule to continuum NS solutions,and fromlow speedmicro-flow to high speed non-equilibrium aerodynamics.The test cases clearly demonstrate tha

关 键 词：Unified scheme non-equilibrium flow Navier-Stokes solution 

分 类 号：O17[理学—数学]