Asymptotic-Preserving scheme for the resolution of evolution equations with stiff transport terms

TL;DR

This paper introduces an asymptotic-preserving numerical scheme for evolution equations with stiff transport terms, enabling accurate long-time simulations in plasma physics models like the Vlasov equation.

Contribution

It presents a novel micro-macro decomposition-based scheme with stabilization, specifically designed to handle stiff transport terms and reduce numerical pollution in long-time regimes.

Findings

Successfully applied to gyrokinetic and Vlasov-Poisson equations

Reduces numerical pollution in long-time simulations

Maintains accuracy across different regimes

Abstract

We develop an asymptotic-preserving scheme to solve evolution problems containing stiff transport terms. This scheme is based to a micro-macro decomposition of the unknown, coupled with a stabilization procedure. The numerical method is applied to the Vlasov equation in the gyrokinetic regime and to the Vlasov-Poisson 1D1V equation, which occur in plasma physics. The asymptotic-preserving properties of our procedure permit to study the long-time behavior of these models. In particular, we limit drastically by this method the numerical pollution, appearing in such time asymptotics when using classical numerical schemes.