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

doi:10.1007/s42967-020-00088-0

摘要/Abstract

摘要： 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 ofer a practical guide for choosing optimal SLDG solvers for linear and nonlinear transport simulations.

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

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 ofer 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

中图分类号:

65M60
65M25

Xiaofeng Cai, Wei Guo, Jing-Mei Qiu. Comparison of Semi-Lagrangian Discontinuous Galerkin Schemes for Linear and Nonlinear Transport Simulations[J]. Communications on Applied Mathematics and Computation, 2022, 4(1): 3-33.

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