Conservative discretization of the Landau collision integral

TL;DR

This paper presents a novel discretization method for the nonlinear Landau collision integral that conserves density, momentum, and energy, applicable to finite-element and discontinuous Galerkin methods without structured meshes.

Contribution

It introduces a conservation-preserving discretization approach for the Landau collision integral compatible with various numerical methods and proves its conservation properties both algebraically and numerically.

Findings

Conservation laws are proven algebraically.

Numerical demonstrations confirm conservation in an axially symmetric relaxation problem.

Method is suitable for finite-element and discontinuous Galerkin implementations.

Abstract

We describe a density-, momentum-, and energy-conserving discretization of the nonlinear Landau collision integral. The method is suitable for both the finite-element and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem using a finite-element implementation.