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dc.contributor.authorDu, Huijing
dc.contributor.authorLiu, Yingjie
dc.contributor.authorLiu, Yuan
dc.contributor.authorXu, Zhiliang
dc.identifier.citationDu, H., Liu, Y., Liu, Y. et al. J Sci Comput (2019)en_US
dc.descriptionClick on the DOI link to access the article (may not be free).en_US
dc.description.abstractThe classical Saint–Venant shallow water equations on complex geometries have wide applications in many areas including coastal engineering and atmospheric modeling. The main numerical challenge in simulating Saint–Venant equations is to maintain the high order of accuracy and well-balanced property simultaneously. In this paper, we propose a high-order accurate and well-balanced discontinuous Galerkin (DG) method on two dimensional (2D) unstructured meshes for the Saint–Venant shallow water equations. The technique used to maintain well-balanced property is called constant subtraction and proposed in Yang et al. (J Sci Comput 63:678–698, 2015). Hierarchical reconstruction limiter with a remainder correction technique is introduced to control numerical oscillations. Numerical examples with smooth and discontinuous solutions are provided to demonstrate the performance of our proposed DG methods.en_US
dc.description.sponsorshipHuijing Du: Research supported in part by NSF Grant DMS-1853636. Yingjie Liu: Research supported in part by NSF Grants DMS-1522585 and DMS-CDS & E-MSS-1622453. Yuan Liu: Research supported in part by a grant from the Simons Foundation (426993). Zhiliang Xu: Research supported in part by NSF Grants DMS-1517293, CDS& E-MSS-1821242 and CDS & E-MSS 1854779.en_US
dc.publisherSpringer USen_US
dc.relation.ispartofseriesJournal of Scientific Computing;2019
dc.subjectConstant subtractionen_US
dc.subjectDiscontinuous Galerkin methodsen_US
dc.subjectHierarchical reconstructionen_US
dc.subjectHyperbolic balance lawsen_US
dc.subjectRemainder correctionen_US
dc.subjectSaint–Venant equationsen_US
dc.subjectShallow water equationsen_US
dc.subjectUnstructured meshesen_US
dc.titleWell-balanced discontinuous Galerkin method for shallow water equations with constant subtraction techniques on unstructured meshesen_US
dc.rights.holder© 2019, Springer Science Business Media, LLC, part of Springer Natureen_US

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