A multiple-relaxation-time collision model by Hermite expansion

Shan, Xiaowen1,2; Li, Xuhui2; Shi, Yangyang2

2021-10-18

10.1098/rsta.2020.0406

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES   影响因子和分区

1364-503X

1471-2962

The Bhatnagar-Gross-Krook (BGK) single-relaxation-time collision model for the Boltzmann equation serves as the foundation of the lattice BGK (LBGK) method developed in recent years. The description of the collision as a uniform relaxation process of the distribution function towards its equilibrium is, in many scenarios, simplistic. Based on a previous series of papers, we present a collision model formulated as independent relaxations of the irreducible components of the Hermite coefficients in the reference frame moving with the fluid. These components, corresponding to the irreducible representation of the rotation group, are the minimum tensor components that can be separately relaxed without violating rotation symmetry. For the 2nd, 3rd and 4th moments, respectively, two, two and three independent relaxation rates can exist, giving rise to the shear and bulk viscosity, thermal diffusivity and some high-order relaxation process not explicitly manifested in the Navier-Stokes-Fourier equations. Using the binomial transform, the Hermite coefficients are evaluated in the absolute frame to avoid the numerical dissipation introduced by interpolation. Extensive numerical verification is also provided. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

lattice Boltzmann equation multiple relaxation time

SCI ; EI

英语

第一 ; 通讯

Science & Technology - Other Topics

Multidisciplinary Sciences

WOS:000692142300013

ROYAL SOC

20213910960714

Distribution functions ; Navier Stokes equations ; Relaxation time ; Viscosity

Fluid Flow, General:631.1 ; Calculus:921.2 ; Statistical Methods:922 ; Probability Theory:922.1 ; Classical Physics; Quantum Theory; Relativity:931 ; Physical Properties of Gases, Liquids and Solids:931.2

PHYSICS

Web of Science

1.Southern Univ Sci & Technol, Guangdong Prov Key Lab Turbulence Res & Applicat, Shenzhen 518055, Peoples R China
2.Southern Univ Sci & Technol, Dept Mech & Aerosp Engn, Shenzhen 518055, Peoples R China

Shan, Xiaowen,Li, Xuhui,Shi, Yangyang. A multiple-relaxation-time collision model by Hermite expansion[J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES,2021,379(2208).

Shan, Xiaowen,Li, Xuhui,&Shi, Yangyang.(2021).A multiple-relaxation-time collision model by Hermite expansion.PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES,379(2208).

Shan, Xiaowen,et al."A multiple-relaxation-time collision model by Hermite expansion".PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 379.2208(2021).