期刊
APPLIED MATHEMATICS AND COMPUTATION
卷 272, 期 -, 页码 291-308出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2015.07.014
关键词
Skew-symmetric shallow water equations; Discontinuous Galerkin spectral element method; Gauss-Lobatto Legendre; Summation-by-parts; Entropy conservation; Well balanced
In this work, we design an arbitrary high order accurate nodal discontinuous Galerkin spectral element type method for the one dimensional shallow water equations. The novel method uses a skew-symmetric formulation of the continuous problem. We prove that this discretisadon exactly preserves the local mass and momentum. Furthermore, we show that combined with a special numerical interface flux function, the method exactly preserves the entropy, which is also the total energy for the shallow water equations. Finally, we prove that the surface fluxes, the skew-symmetric volume integrals, and the source term are well balanced. Numerical tests are performed to demonstrate the theoretical findings. (C) 2015 Elsevier Inc. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据