A comparison of two entropy stable discontinuous Galerkin spectral element approximations for the shallow water equations with non-constant topography
A comparison of two entropy stable discontinuous Galerkin spectral element approximations for the shallow water equations with non-constant topography
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DOI：
10.1016/j.jcp.2015.08.034
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发表时间：
2015-11
期刊：
影响因子：
--
通讯作者：
A. R. Winters;G. Gassner
中科院分区：
文献类型：
--
作者：
A. R. Winters;G. Gassner
在这项工作中，我们比较和对比两个可证明的熵稳定和高阶精度的节块间断Galerkin谱元方法应用于一维浅水方程的非恒定地形问题。对于浅水方程的数值近似，特别重要的是良好平衡的性质。良好平衡的属性是一个属性，数值近似可以保持恒定的水高度在底部地形的存在下的稳态解。数值试验进行了探索的相似性和差异性，在两个高阶格式。
In this work, we compare and contrast two provably entropy stable and high-order accurate nodal discontinuous Galerkin spectral element methods applied to the one dimensional shallow water equations for problems with non-constant bottom topography. Of particular importance for numerical approximations of the shallow water equations is the well-balanced property. The well-balanced property is an attribute that a numerical approximation can preserve a steady-state solution of constant water height in the presence of a bottom topography. Numerical tests are performed to explore similarities and differences in the two high-order schemes.