Development of explicit formulations of G45-based gas kinetic scheme for simulation of continuum and rarefied flows

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

2022-04-04

10.1103/PhysRevE.105.045302

PHYSICAL REVIEW E   影响因子和分区

2470-0045

2470-0053

In this work, the explicit formulations of the Grad's distribution function for the 45 moments (G45)-based gas kinetic scheme (GKS) are presented. Similar to the G13 function-based gas kinetic scheme (G13-GKS), G45GKS simulates flows from the continuum regime to the rarefied regime by solving the macroscopic governing equations based on the conservation laws, which are widely used in conventional Navier-Stokes solver. These macroscopic governing equations are discretized by the finite volume method, where the numerical fluxes are evaluated by the local solution to the Boltzmann equation. The initial distribution function is reconstructed by the G45 distribution function, which is a higher order truncation of the Hermite expansion of distribution function compared with the G13 distribution function. Such high order truncation of Hermite expansion helps the present solver to achieve a better accuracy than G13-GKS. Moreover, the reconstruction of distribution function makes the development of explicit formulations of numerical fluxes feasible, and the evolution of the distribution function, which is the main reason why the discrete velocity method is expensive, is avoided. Several numerical experiments are performed to examine the accuracy of G45-GKS. Results show that the accuracy of the present solver for almost all flow problems is much better than G13-GKS. Moreover, some typical rarefied effects, such as the direction of heat flux without temperature gradients and thermal creep flow, can be well captured by the solver.

SCI ; EI

英语

通讯

Physics

Physics, Fluids & Plasmas ; Physics, Mathematical

WOS:000786497300003

AMER PHYSICAL SOC

20221712030183

Boltzmann equation ; Creep ; Finite volume method ; Heat flux ; Kinetics ; Navier Stokes equations ; Numerical methods

Fluid Flow, General:631.1 ; Heat Transfer:641.2 ; Calculus:921.2 ; Numerical Methods:921.6 ; Statistical Methods:922 ; Probability Theory:922.1 ; Classical Physics; Quantum Theory; Relativity:931 ; Materials Science:951

PHYSICS

Web of Science

1.Natl Univ Singapore, Dept Mech Engn, 10 Kent Ridge Crescent, Singapore 119260, Singapore
2.Southern Univ Sci & Technol, Dept Mech & Aerosp Engn, Shenzhen 518055, Peoples R China
3.Nanjing Univ Aeronaut & Astronaut, Dept Aerodynam, Coll Aerosp Engn, Yudao St, Nanjing 210016, Jiangsu, Peoples R China

Liu, Z. J.,Shu, C.,Chen, S. Y.,et al. Development of explicit formulations of G45-based gas kinetic scheme for simulation of continuum and rarefied flows[J]. PHYSICAL REVIEW E,2022,105(4).

Liu, Z. J.,Shu, C.,Chen, S. Y.,Liu, W.,Yuan, Z. Y.,&Yang, L. M..(2022).Development of explicit formulations of G45-based gas kinetic scheme for simulation of continuum and rarefied flows.PHYSICAL REVIEW E,105(4).

Liu, Z. J.,et al."Development of explicit formulations of G45-based gas kinetic scheme for simulation of continuum and rarefied flows".PHYSICAL REVIEW E 105.4(2022).