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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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Authors and Affiliations

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

    Xiaofeng Cai & Jing-Mei Qiu

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

    Wei Guo

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  1. Xiaofeng Cai
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  2. Wei Guo
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Correspondence to Wei Guo.

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W. Guo: Research is supported by NSF grant NSF-DMS-1830838.

J.-M. Qiu: Research is supported by NSF grant NSF-DMS-1522777 and NSF-DMS-1818924, Air Force Office of Scientific Computing FA9550-18-1-0257.

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Cai, X., Guo, W. & Qiu, JM. Comparison of Semi-Lagrangian Discontinuous Galerkin Schemes for Linear and Nonlinear Transport Simulations. Commun. Appl. Math. Comput. 4, 3–33 (2022). https://doi.org/10.1007/s42967-020-00088-0

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