Eulerian--Lagrangian Runge--Kutta Discontinuous Galerkin Method for Transport Simulations on Unstructured Meshes

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Author(s)Cai, Xiaofeng
Author(s)Qiu, Jing-Mei
Date Accessioned2022-08-16T15:19:35Z
Date Available2022-08-16T15:19:35Z
Publication Date2022-07-26
DescriptionThis article was originally published in SIAM Journal on Scientific Computing. The version of record is available at: https://doi.org/10.1137/21M1456753.en_US
AbstractThe semi-Lagrangian (SL) approach is attractive in transport simulations, e.g., in climate modeling and kinetic models, due to its numerical stability in allowing extra-large time-stepping sizes. For practical problems with complex geometry, schemes on the unstructured meshes are preferred. However, accurate and mass conservative SL methods on unstructured meshes are still under development and encounter several challenges. For instance, when tracking characteristics backward in time, high order curves are required to accurately approximate the shape of upstream cells, which brings in extra computational complexity. To avoid such computational complexity, we propose an Eulerian--Lagrangian Runge--Kutta discontinuous Galerkin method (EL RK DG) in [X. Cai, J.-M. Qiu, and Y. Yang, J. Comput. Phys., 439 (2021), 110392] as an extension of the SL discontinuous Galerkin (DG) methods. This work is a further extension of the algorithm to unstructured triangular meshes with discussion on the treatment of the inflow boundary condition. We also discuss the discrete geometric conservation law. The nonlinear weighted essentially nonoscillatory (WENO) limiter is applied to control oscillations. Desired properties of the proposed method are numerically verified by a set of benchmark tests.en_US
SponsorThis work was supported by NSF grant DMS-1818924, by Air Force Office of Scientific Research grant FA9550-18-1-0257, and by the University of Delaware.en_US
CitationCai, Xiaofeng, and Jing-Mei Qiu. “Eulerian--Lagrangian Runge--Kutta Discontinuous Galerkin Method for Transport Simulations on Unstructured Meshes.” SIAM Journal on Scientific Computing 44, no. 4 (2022): A2037–60. https://doi.org/10.1137/21M1456753.en_US
ISSN1095-7197
URLhttps://udspace.udel.edu/handle/19716/31200
Languageen_USen_US
PublisherSIAM Journal on Scientific Computingen_US
KeywordsEulerian--Lagrangianen_US
Keywordsdiscontinuous Galerkinen_US
Keywordsunstructured triangular meshesen_US
Keywordsmass conservationen_US
Keywordssemi-Lagrangianen_US
Keywordscharacteristicsen_US
TitleEulerian--Lagrangian Runge--Kutta Discontinuous Galerkin Method for Transport Simulations on Unstructured Meshesen_US
TypeArticleen_US
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