Practical evaluation of five partly discontinuous finite element pairs for the non‐conservative shallow water equations
Practical evaluation of five partly discontinuous finite element pairs for the non‐conservative shallow water equations
复制标题
非保守浅水方程的五个部分不连续有限元对的实际评估
DOI：
10.1002/fld.2094
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发表时间：
2009
影响因子：
1.8
通讯作者：
V. Legat
中科院分区：
文献类型：
--
作者：
Richard Comblen;J. Lambrechts;J. Remacle;V. Legat
本文对浅水方程的五种有限元对进行了比较。我们考虑连续，不连续和部分不连续的有限元公式，应该提供二阶空间精度。所有这些都依赖于相同的弱公式，使用黎曼求解器来计算界面积分。我们定义了浅水方程在其参数空间内的几种渐近极限情形。我们的想法是在亚临界浅水流的几个相关区域中对这些数值方案进行比较。最后，提出了一个新的对，使用速度和高程的非协调线性元素（P NC1 −P NC1），在所有测试用例中给出了最佳收敛速度。P NC1 −P1和P DG1 −P1混合公式对无粘流缺乏收敛性。P DG1 −P2对更昂贵，但为所有基准测试提供准确的结果。P DG1 −P DG1提供了一个有效的选择，除了无粘科里奥利支配流，在那里观察到收敛的小缺乏。版权所有© 2009约翰威利父子有限公司。
This paper provides a comparison of five finite element pairs for the shallow water equations. We consider continuous, discontinuous and partially discontinuous finite element formulations that are supposed to provide second‐order spatial accuracy. All of them rely on the same weak formulation, using Riemann solver to evaluate interface integrals. We define several asymptotic limit cases of the shallow water equations within their space of parameters. The idea is to develop a comparison of these numerical schemes in several relevant regimes of the subcritical shallow water flow. Finally, a new pair, using non‐conforming linear elements for both velocities and elevation (P NC1 −P NC1 ), is presented, giving optimal rates of convergence in all test cases. P NC1 −P1 and P DG1 −P1 mixed formulations lack convergence for inviscid flows. P DG1 −P2 pair is more expensive but provides accurate results for all benchmarks. P DG1 −P DG1 provides an efficient option, except for inviscid Coriolis‐dominated flows, where a small lack of convergence is observed. Copyright © 2009 John Wiley & Sons, Ltd.
影响因子：
3.2
作者：
Colin J. Cotter;David A. Ham;Christopher C. Pain
通讯作者：
Colin J. Cotter;David A. Ham;Christopher C. Pain
DOI：
10.1016/j.jcp.2008.09.014
发表时间：
2009-01
期刊：
J. Comput. Phys.
影响因子：
--
作者：
C. Cotter;D. Ham;C. Pain;S. Reich
通讯作者：
C. Cotter;D. Ham;C. Pain;S. Reich