A new macroscopic model derived from the Boltzmann equation and the discontinuous Galerkin method for solving kinetic equations

TL;DR

This paper introduces a new macroscopic model derived from the Boltzmann equation that ensures conservation laws and aligns with the discontinuous Galerkin method, simplifying the solution of kinetic equations.

Contribution

The paper presents a novel macroscopic model derived from the Boltzmann equation that guarantees conservation laws and matches the DG method's system, offering a new approach for kinetic equations.

Findings

Model guarantees mass, momentum, energy conservation

Equations coincide with DG method applied to Boltzmann

Simplifies solving kinetic equations

Abstract

We propose a new macroscopic model derived from the classical nonlinear Boltzmann equation. A set of partial differential equations is obtained easily. The unknowns depend on the time and space coordinates, and are related to the distribution function, which is the unknown of the Boltzmann equation. This new model guarantees the conservation of the mass, momentum and energy. We prove that the set of equations coincides with the system obtained applying the discontinuous Galerkin method to the Boltzmann equation (see A. Majorana, Kinetic and Related models, 4 (2011), 139--151).