Well-balanced discontinuous Galerkin method for shallow water equations with constant subtraction techniques on unstructured meshes

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Authors
Du, Huijing
Liu, Yingjie
Liu, Yuan
Xu, Zhiliang
Advisors
Issue Date
2019-10
Type
Article
Keywords
Constant subtraction , Discontinuous Galerkin methods , Hierarchical reconstruction , Hyperbolic balance laws , Remainder correction , Saint–Venant equations , Shallow water equations , Unstructured meshes
Research Projects
Organizational Units
Journal Issue
Citation
Du, H., Liu, Y., Liu, Y. et al. J Sci Comput (2019)
Abstract

The 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.

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Publisher
Springer US
Journal
Book Title
Series
Journal of Scientific Computing;2019
PubMed ID
DOI
ISSN
0885-7474
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