Work

Discretization of the Velocity Space in the Solution of the Boltzmann Equation

Year: 1998

Type: article

Abstract: We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite polynomial expansion. Discretizing the Boltzmann equation with a Bhatnagar-Gross-Krook collision term at the velocities that correspond to the nodes of a Hermite quadrature is shown to be equivalent to truncating the Hermite expansion of the distribution function to the corresponding order. The truncated part of the distribution has no contribution to the moments of low orders and is negligible at small Mach numbers.

Source: Physical Review Letters

DOI: 10.1103/physrevlett.80.65

Authors: Xiaowen Shan, Xiaoyi He

Institutions: United States Air Force Research Laboratory, Los Alamos National Laboratory, Hanscom Air Force Base

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W1969064103

FWCI: 6.408

Cites: 19

Cited by: 447

Related to: 10