High Order Semi-Lagrangian WENO Method for Kinetic
Equations and Applications in Plasma Physics
Prof. Jingmei Qiu
Department of Mathematical and Computer Science
Colorado School of Mines, Golden, CO 80401
Date: 10/08/2010
Abstract
We propose a novel semi-Lagrangian finite difference formulation for approximating
conservative form of advection equations with general variable coefficients. Compared with the
traditional semi-Lagrangian finite difference schemes, which are designed by approximating the
advective form of equation via direct characteristics tracing, the scheme we proposed
approximates the conservative form of equation. This essential difference makes the proposed
scheme conservative by nature, and extendable to equations with variable coefficients. The
proposed semi-Lagrangian finite difference framework is coupled with high order essentially
non-oscillatory (ENO) or weighted ENO (WENO) reconstructions to achieve high order
accuracy in smooth parts of the solution and capture sharp interfaces without introducing
oscillations. The scheme is extended to high dimensional problem by Strang splitting. The
performance of the proposed schemes is demonstrated by linear advection, several challenging
examples of rigid body rotation and swirling deformation in multi-dimensions, as well as the
Vlasov Poisson system for plasma applications. As the information is propagating along
characteristics, the semi-Lagrangian scheme does not have CFL time step restriction, allowing
for a cheaper and more flexible numerical realization than the regular finite difference scheme.