Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field
This work addresses the challenge of simulating highly-oscillatory plasma dynamics with non-homogeneous magnetic fields, which is relevant for computational plasma physics.
The authors develop uniformly accurate numerical methods for Vlasov and Vlasov-Poisson equations with non-homogeneous strong magnetic fields, achieving insensitivity to stiffness in accuracy and computational cost. The methods are validated on several numerical examples.
In this paper, we consider the numerical solution of highly-oscillatory Vlasov and Vlasov-Poisson equations with non-homogeneous magnetic field. Designed in the spirit of recent uniformly accurate methods, our schemes remain insensitive to the stiffness of the problem, in terms of both accuracy and computational cost. The specific difficulty (and the resulting novelty of our approach) stems from the presence of a non-periodic oscillation, which necessitates a careful ad-hoc reformulation of the equations. Our results are illustrated numerically on several examples.