No. 2020.04
Entropic quadrature for moment approximations of the Boltzmann-BGK equation
N. Böhmer and M. Torrilhon
Subject: Problem of moments, Boltzmann equation, fluid dynamics, maximum-entropy closure, quadrature method of moments, discontinuous Galerkin method

Abstract

Using the method of moments to approximate the solution of kinetic equations has become a standard technique especially in the context of solving the Boltzmann equation to model rarefied gases. One attractive example is the maximum-entropy closure, which, however, is computationally barely affordable. In this paper, we will combine the maximum-entropy approach with the quadrature method of moments (QMOM) – two methods which have in some sense diametric properties, thereby introducing the “Entropic Quadrature” (EQ) closure. EQ calculates a sparse quadrature-based reconstruction of the unknown velocity distribution like the QMOM where the physical meaningful maximum-entropy principle is employed as a criterion for selecting a quadrature among different quadratures fitting the given moments. We will discuss the construction of the closure and give several numerical examples of its performance in one and two dimensions.

Reference

J. Comput. Phys. 401 (2020), 108992, 25 pp.