A structure-preserving particle discretisation for the Lenard-Bernstein collision operator

TL;DR

This paper introduces a novel macro-particle discretisation method for the Lenard-Bernstein collision operator in plasma modeling, ensuring energy and momentum conservation in numerical simulations.

Contribution

It presents a structure-preserving particle discretisation that maintains the physical laws of thermodynamics for the Lenard-Bernstein operator.

Findings

Discretisation preserves energy and momentum.

Method improves physical accuracy of plasma simulations.

Enhances numerical stability and fidelity.

Abstract

Collisions are an important dissipation mechanism in plasmas. In one-dimensional modelling, a commonly used collision operator is the Lenard-Bernstein operator, or its modified energy- and momentum-conserving counterpart. When approximating such operators numerically, it is important to respect their structure in order to satisfy the laws of thermodynamics. It is, however, challenging to discretise such operators in a structure-preserving way when considering particle methods. In this work, we present a macro-particle discretisation of the Lenard-Bernstein collision operator that is energy and momentum preserving.