Asymptotic-Preserving scheme for the resolution of evolution equations with stiff transport terms
Provides a numerical method for plasma physics simulations that maintains accuracy over long times, addressing a known bottleneck in classical schemes.
Developed an asymptotic-preserving scheme for evolution equations with stiff transport terms, applied to Vlasov and Vlasov-Poisson equations. The method reduces numerical pollution in long-time simulations.
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.