Nonoscillatory interpolation methods applied to Vlasov-based models

We demonstrate the ability of nonoscillatory interpolation strategies for solving efficiently the transport phase in kinetic systems with applications to charged particle transport in plasmas and semiconductors. Pointwise weighted essentially nonoscillatory (PWENO) interpolation is applied to obtain semi-Lagrangian and flux balance methods that together with splitting techniques form the building blocks of our numerical approach. These methods do not present the restrictive CFL condition typical of finite-difference methods with explicit time-solvers, and, moreover, they provide reliable results controlling parasite oscillations from classical polynomial interpolation while giving highly accurate approximations of smooth parts of the solutions. We perform and compare these methods in different benchmark problems for Vlasov or collisional models for charged particle transport. © 2007 Society for Industrial and Applied Mathematics.