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

被引：0
作者：
Huijing Du
Yingjie Liu
Yuan Liu
Zhiliang Xu
机构：
[1] University of Nebraska-Lincoln,Department of Mathematics
[2] Georgia Institute of Technology,School of Mathematics
[3] Wichita State University,Department of Mathematics, Statistics and Physics
[4] University of Notre Dame,Department of Applied and Computational Mathematics and Statistics
来源：
Journal of Scientific Computing | 2019年 / 81卷
关键词：
Hyperbolic balance laws; Saint–Venant equations; Shallow water equations; Discontinuous Galerkin methods; Constant subtraction; Unstructured meshes; Hierarchical reconstruction; Remainder correction;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：2115 / 2131
页数：16
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