Conservative Closures of the Vlasov-Poisson Equations Based on Symmetrically Weighted Hermite Spectral Expansion

TL;DR

This paper develops conservative closure methods for the Vlasov-Poisson equations using symmetrically weighted Hermite spectral expansion, ensuring preservation of key properties and validating through numerical simulations of Langmuir waves.

Contribution

It introduces a novel conservative closure approach based on Hermite spectral expansion that maintains hyperbolicity and anti-symmetry in discretized Vlasov-Poisson equations.

Findings

Closure by truncation is most suitable for the Hermite formulation.

Numerical simulations confirm the analytical properties of the closure.

Conservative closures preserve key physical properties during discretization.

Abstract

We derive conservative closures of the Vlasov-Poisson equations discretized in velocity via the symmetrically weighted Hermite spectral expansion. The short note analyzes the conservative closures preservation of the hyperbolicity and anti-symmetry of the Vlasov equation. Furthermore, we verify numerically the analytically derived conservative closures on simulating a classic electrostatic benchmark problem: the Langmuir wave. The numerical results and analytic analysis show that the closure by truncation is the most suitable conservative closure for the symmetrically weighted Hermite formulation.