Comparison of semi-Lagrangian discontinuous Galerkin schemes for linear and nonlinear transport simulations
It offers a practical guide for researchers and engineers choosing SLDG methods for transport problems, but the comparison is incremental and does not introduce new algorithms or achieve breakthrough performance.
This paper reviews and compares semi-Lagrangian discontinuous Galerkin (SLDG) methods for linear and nonlinear transport simulations, focusing on splitting versus non-splitting approaches. Through extensive numerical tests, it provides practical guidance for selecting optimal SLDG solvers.
Transport problems arise across diverse fields of science and engineering. Semi-Lagrangian (SL) discontinuous Galerkin (DG) methods are a class of high order deterministic transport solvers that enjoy advantages of both SL approach and DG spatial discretization. In this paper, we review existing SLDG methods to date and compare numerical their performances. 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.