Explicit formulations of G13-based gas kinetic flux solver (G13-GKFS) for simulation of continuum and rarefied flows

Liu，Z. J.1,2; Yang，L. M.3; Shu，C.1; Chen，S. Y.2; Wan，M. P.2; Liu，W.1; Yuan，Z. Y.4

2021-03-01

10.1063/5.0044295

PHYSICS OF FLUIDS   影响因子和分区

1070-6631

1089-7666

In this work, the explicit formulations of the Grad's distribution function for 13 moments (G13)-based gas kinetic flux solver (GKFS) for simulation of flows from the continuum regime to the rarefied regime are presented. The present solver retains the framework of GKFS, and it combines some good features of the discrete velocity method (DVM) and moment method. In the G13-GKFS, the macroscopic governing equations are first discretized by the finite volume method, and the numerical fluxes are evaluated by the local solution of the Boltzmann equation. To reconstruct the local solution of the Boltzmann equation, the initial distribution function is reconstructed by the Grad's distribution function for 13 moments, which enables the G13-GKFS to simulate flows in the rarefied regime. Thanks to this reconstruction, the evolution of distribution function is avoided, and the numerical fluxes can be expressed by explicit formulations. Therefore, the computational efficiency of G13-GKFS is much higher than that of DVM. The accuracy and computational efficiency of the present solver in explicit form are examined by several numerical examples. Numerical results show that the present solver can predict accurate results for flows in the continuum regime and reasonable results for flows in the rarefied regime. More importantly, the central processing unit time of the present solver is about 1% of that of DVM for two-dimensional (2D) microflow problems, and it is about twice of the conventional Navier-Stokes solver for 2D continuum flows.

SCI ; EI

英语

其他

WOS:000636334900001

20211410171885

Boltzmann equation ; Digital voltmeters ; Distribution functions ; Efficiency ; Finite volume method ; Kinetic theory of gases ; Method of moments ; Navier Stokes equations ; Numerical methods ; Program processors

Production Engineering:913.1 ; Mathematics:921 ; Statistical Methods:922 ; Probability Theory:922.1 ; Electric and Electronic Instruments:942.1

PHYSICS

2-s2.0-85103443470

Scopus

1.Department of Mechanical Engineering,National University of Singapore,10 Kent Ridge Crescent,119260,Singapore
2.Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,518055,China
3.Department of Aerodynamics,College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing, Jiangsu,Yudao Street,210016,China
4.Department of Aeronautics and Astronautics,Zhejiang University,Hangzhou,310027,China

Liu，Z. J.,Yang，L. M.,Shu，C.,et al. Explicit formulations of G13-based gas kinetic flux solver (G13-GKFS) for simulation of continuum and rarefied flows[J]. PHYSICS OF FLUIDS,2021,33(3).

Liu，Z. J..,Yang，L. M..,Shu，C..,Chen，S. Y..,Wan，M. P..,...&Yuan，Z. Y..(2021).Explicit formulations of G13-based gas kinetic flux solver (G13-GKFS) for simulation of continuum and rarefied flows.PHYSICS OF FLUIDS,33(3).

Liu，Z. J.,et al."Explicit formulations of G13-based gas kinetic flux solver (G13-GKFS) for simulation of continuum and rarefied flows".PHYSICS OF FLUIDS 33.3(2021).