General synthetic iterative scheme for nonlinear gas kinetic simulation of multi-scale rarefied gas flows

Zhu，Lianhua1; Pi，Xingcai2; Su，Wei3; Li，Zhi Hui2,4; Zhang，Yonghao3; Wu，Lei5

2021-04-01

10.1016/j.jcp.2020.110091

JOURNAL OF COMPUTATIONAL PHYSICS   影响因子和分区

0021-9991

1090-2716

The general synthetic iterative scheme (GSIS) is extended to find the steady-state solution of the nonlinear gas kinetic equation, resolving the long-standing problems of slow convergence and requirement of ultra-fine grids in near-continuum flows. The key ingredient of GSIS is the tight coupling of gas kinetic and macroscopic synthetic equations, where the constitutive relations explicitly contain Newton's law of shear stress and Fourier's law of heat conduction. The higher-order constitutive relations describing rarefaction effects are calculated from the velocity distribution function; however, their constructions are simpler than our previous work (Su et al., 2020 [28]) for linearized gas kinetic equations. On the other hand, solutions of macroscopic synthetic equations are used to accelerate the evolution of gas kinetic equation at the next iteration step. A rigorous linear Fourier stability analysis of the present schemes in periodic system shows that the error decay rate of GSIS can be smaller than 0.5, which means that the deviation to steady-state solution can be reduced by 3 orders of magnitude in 10 iterations. Other important advantages of the GSIS are: (i) it does not rely on the specific form of Boltzmann collision operator, and (ii) it can be solved by sophisticated techniques in computational fluid dynamics, making it amenable to large scale engineering applications. In this paper, the efficiency and accuracy of GSIS are demonstrated by a number of canonical test cases in rarefied gas dynamics, covering different flow regimes. (C) 2020 Elsevier Inc. All rights reserved.

Gas kinetic equation Multi-scale rarefied gas flows Fourier stability analysis General synthetic iterative scheme Fast convergence

SCI ; EI

英语

通讯

European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie[793007] ; Engineering and Physical Sciences Research Council in the UK["EP/R041938/1","EP/M021475/1","EP/R029581/1"] ; National Natural Science Foundation of China[91530319]

Computer Science ; Physics

Computer Science, Interdisciplinary Applications ; Physics, Mathematical

WOS:000623416900013

ACADEMIC PRESS INC ELSEVIER SCIENCE

20210609895116

Computational fluid dynamics ; Decay (organic) ; Distribution functions ; Gas dynamics ; Gases ; Heat conduction ; Integral equations ; Iterative methods ; Kinetic energy ; Kinetics ; Nonlinear equations ; Shear stress

Gas Dynamics:631.1.2 ; Heat Transfer:641.2 ; Biochemistry:801.2 ; Calculus:921.2 ; Numerical Methods:921.6 ; Probability Theory:922.1 ; Classical Physics; Quantum Theory; Relativity:931 ; Mechanics:931.1

PHYSICS

Web of Science

1.James Weir Fluids Laboratory,Department of Mechanical and Aerospace Engineering,University of Strathclyde,Glasgow,G1 1XJ,United Kingdom
2.Hypervelocity Aerodynamics Institute,China Aerodynamics Research and Development Center,Mianyang,621000,China
3.School of Engineering,University of Edinburgh,Edinburgh,EH9 3FB,United Kingdom
4.National Laboratory of Computational Fluid Dynamics,Beijing,100191,China
5.Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,518055,China

Zhu，Lianhua,Pi，Xingcai,Su，Wei,et al. General synthetic iterative scheme for nonlinear gas kinetic simulation of multi-scale rarefied gas flows[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2021,430.

Zhu，Lianhua,Pi，Xingcai,Su，Wei,Li，Zhi Hui,Zhang，Yonghao,&Wu，Lei.(2021).General synthetic iterative scheme for nonlinear gas kinetic simulation of multi-scale rarefied gas flows.JOURNAL OF COMPUTATIONAL PHYSICS,430.

Zhu，Lianhua,et al."General synthetic iterative scheme for nonlinear gas kinetic simulation of multi-scale rarefied gas flows".JOURNAL OF COMPUTATIONAL PHYSICS 430(2021).