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Well-Balanced Discontinuous Galerkin Method for Shallow Water Equations with Constant Subtraction Techniques on Unstructured Meshes

  • Huijing Du
  • Yingjie Liu
  • Yuan LiuEmail author
  • Zhiliang Xu
Article
  • 30 Downloads

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.

Keywords

Hyperbolic balance laws Saint–Venant equations Shallow water equations Discontinuous Galerkin methods Constant subtraction Unstructured meshes Hierarchical reconstruction Remainder correction 

Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Department of Mathematics, Statistics and PhysicsWichita State UniversityWichitaUSA
  4. 4.Department of Applied and Computational Mathematics and StatisticsUniversity of Notre DameNotre DameUSA

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