Structure preservation using discrete gradients in the Vlasov-Poisson-Landau system

TL;DR

This paper introduces a structure-preserving numerical framework for the Vlasov-Poisson-Landau system that conserves key physical quantities and entropy, combining particle-in-cell discretization with discrete gradient time integrators.

Contribution

It develops a novel scheme that guarantees conservation of mass, momentum, energy, and entropy monotonicity for the Vlasov-Poisson-Landau system using discrete gradient integrators.

Findings

Conserves mass, momentum, and energy exactly.

Preserves entropy production monotonicity.

Demonstrates structure-preserving properties with PETSc implementation.

Abstract

We present a novel structure-preserving framework for solving the Vlasov-Poisson-Landau system of equations using a particle in cell (PIC) discretization combined with discrete gradient time integrators. The Vlasov-Poisson-Landau system is an accurate model for studying hot plasma dynamics at a kinetic scale where small-angle Coulomb collisions dominate. Our scheme guarantees conservation of mass, momentum and energy as well as preservation of the monotonicity of entropy production in both the time-continuous and discrete systems. We employ the conservative integrator for both the Hamiltonian Vlasov-Poisson equations and the dissipative Landau equation using the PETSc library (www.mcs.anl.gov/petsc) to showcase structure-preserving properties.