Metriplectic particle-in-cell integrators for the Landau collision operator

TL;DR

This paper introduces a novel particle-in-cell integrator framework leveraging the metriplectic structure to accurately and efficiently simulate the nonlinear Landau collision operator, ensuring conservation laws and entropy production.

Contribution

It develops a new finite-dimensional, time-continuous metriplectic system for macro particle weights using discrete gradients, compatible with existing Poisson integrators.

Findings

Conserves density, momentum, and energy algebraically.

Ensures positive semi-definite entropy production.

Compatible with Vlasov-Maxwell particle-in-cell methods.

Abstract

In this paper, we present a new framework for addressing the nonlinear Landau collision operator in terms of particle-in-cell methods. We employ the underlying metriplectic structure of the collision operator and, using a macro particle discretization for the distribution function, we transform the infinite-dimensional system into a finite-dimensional time-continuous metriplectic system for advancing the macro particle weights. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of density, momentum, and energy, as well as the positive semi-definite production of entropy in both the time-continuous and the fully discrete system is demonstrated algebraically. The new algorithm is fully compatible with the existing particle-in-cell Poisson integrators for the Vlasov-Maxwell system.