Communications on Applied Mathematics and Computation, 2022, 4(1): 3-33

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

Xiaofeng Cai1, Wei Guo2, Jing-Mei Qiu1

1. Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA;

2. Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 70409, USA

Abstract: Transport problems arise across diverse felds 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 the SL approach and the DG spatial discretization. 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 nonsplitting 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.

Key words: Semi-Lagrangian (SL), Discontinuous Galerkin (DG), Transport simulations, Splitting, Non-splitting, Comparison

https://link.springer.com/article/10.1007/s42967-020-00088-0