Raviart–Thomas and Brezzi–Douglas–Marini finite‐element approximations of the shallow‐water equations
Raviart–Thomas and Brezzi–Douglas–Marini finite‐element approximations of the shallow‐water equations
复制标题
浅水方程的 Raviart-Thomas 和 Brezzi-Douglas-Marini 有限元近似
DOI：
10.1002/fld.1668
复制
发表时间：
2008
影响因子：
1.8
通讯作者：
D. Y. Le Roux
中科院分区：
文献类型：
--
作者：
V. Rostand;D. Y. Le Roux
本文介绍了用Raviart-Thomas和Brezzi-Douglas-Marini有限元对离散浅水方程的分析。对于惯性重力波，为了量化格式在等边三角形和偏置三角形两种网格上的色散性质，得到了离散公式并计算了色散关系。用线性代数方法来确定离散化过程中可能存在的伪模态。对地转平衡进行了研究，并在结构网格和非结构网格上对最小的可表示涡进行了表征。模拟重力模态和罗斯比模态的两个试验问题的数值解与解析结果吻合较好。版权所有©2007 John Wiley & Sons， Ltd
An analysis of the discrete shallow‐water equations using the Raviart–Thomas and Brezzi–Douglas–Marini finite elements is presented. For inertia–gravity waves, the discrete formulations are obtained and the dispersion relations are computed in order to quantify the dispersive nature of the schemes on two meshes made up of equilateral and biased triangles. A linear algebra approach is also used to ascertain the possible presence of spurious modes arising from the discretization. The geostrophic balance is examined and the smallest representable vortices are characterized on both structured and unstructured meshes. Numerical solutions of two test problems to simulate gravity and Rossby modes are in good agreement with the analytical results. Copyright © 2007 John Wiley & Sons, Ltd.