Well-Balanced Discontinuous Galerkin Method for Shallow Water Equations with Constant Subtraction Techniques on Unstructured Meshes
Well-Balanced Discontinuous Galerkin Method for Shallow Water Equations with Constant Subtraction Techniques on Unstructured Meshes
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DOI：
10.1007/s10915-019-01073-3
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发表时间：
2019-11
影响因子：
2.5
通讯作者：
H. Du;Yingjie Liu;Yuan Liu;Zhiliang Xu
中科院分区：
文献类型：
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作者：
H. Du;Yingjie Liu;Yuan Liu;Zhiliang Xu
复杂几何条件下的经典圣维南浅水方程在海岸工程和大气模拟等领域有着广泛的应用。数值模拟圣维南方程的主要挑战是同时保持高精度和良好的平衡性。本文提出了一种求解二维非结构网格上Saint-Venant浅水波方程的高精度平衡间断Galerkin（DG）方法。用于保持良好平衡的性质的技术被称为常数减法，并且在Yang等人（J Sci Comput 63：678-698，2015）中提出。引入带余数修正技术的分层重构限幅器来控制数值振荡。光滑和不连续的解决方案的数值例子来证明我们提出的DG方法的性能。
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.