Adaptive one-step discontinuous Galerkin method for Vlasov systems

We present an adaptive high order one-step discontinuous Galerkin (DG) method for Vlasov-Poisson and relativistic Vlasov-Maxwell systems, which describe single-species and multi-species collisionless plasma. This method is formulated in prediction-correction style, where the prediction is a regionally implicit reconstruction of mixed spacetime derivatives, inspired by Guthrey and Rossmanith (2019), and the correction is an explicit update, following Gassner et al. (2011). Different from conventional DG methods for Vlasov systems, this is an unsplit timestepping scheme with linearized electromagnetic field, which permits an efficient parallel implementation without computationally expensive nonlinear solvers. Further, a mass-conserving, p-adaptive DG discretization is developed for the distribution functions such that the solutions provide more subcell details in regions of interest.

We have implemented this method in distributed-shared memory C++ code, powered by MPI and OpenMP. We present numerical studies such as two stream instability, Landau damping, ion-acoustic shock wave, and Weibel instability.