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

Xiaofeng Cai; Wei Guo; Jing-Mei Qiu

doi:10.1007/s42967-020-00088-0

Communications on Applied Mathematics and Computation ›› 2020, Vol. 4 ›› Issue (1) : 3 -33. DOI: 10.1007/s42967-020-00088-0

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

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Abstract

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 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 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.

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Xiaofeng Cai, Wei Guo, Jing-Mei Qiu. Comparison of Semi-Lagrangian Discontinuous Galerkin Schemes for Linear and Nonlinear Transport Simulations. Communications on Applied Mathematics and Computation, 2020, 4(1): 3-33 DOI:10.1007/s42967-020-00088-0