Comparison of Semi-Lagrangian Discontinuous Galerkin Schemes for Linear and Nonlinear Transport Simulations

Transport problems arise across diverse fields of science and engineering.Semi-Lagran-gian(SL)discontinuous Galerkin(DG)methods are a class of high-order deterministic transport solvers that enjoy advantages of both the SL approach and the DG spatial discre-tization.In this paper,we review existing SLDG methods to date and compare numerically their performance.In particular,we make a comparison between the splitting and non-splitting SLDG methods for multi-dimensional transport simulations.Through extensive numerical results,we offer a practical guide for choosing optimal SLDG solvers for linear and nonlinear transport simulations.