A deterministic numerical model for the nonlinear Boltzmann equation

TL;DR

This paper introduces a deterministic discontinuous Galerkin scheme for solving the nonlinear Boltzmann equation, ensuring conservation laws without stochastic methods, advancing numerical approaches for rarefied gas dynamics.

Contribution

The paper presents a novel deterministic numerical scheme based on discontinuous Galerkin methods that conserves physical quantities without stochastic collision treatments.

Findings

Conserves mass, momentum, and energy exactly.

Avoids stochastic procedures in collision operator treatment.

Provides a reliable deterministic alternative for Boltzmann equation simulation.

Abstract

We propose a new deterministic numerical scheme, based on the discontinuous Galerkin method, for solving the Boltzamnn equation for rarefied gases. The new scheme guarantees the conservation of the mass, momentum and energy. We avoid any stochastic procedures in the treatment of the collision operator of the Boltzmamn equation.