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Practical evaluation of five partly discontinuous finite element pairs for the non‐conservative shallow water equations
Author(s) -
Comblen Richard,
Lambrechts Jonathan,
Remacle JeanFrançois,
Legat Vincent
Publication year - 2009
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2094
Subject(s) - inviscid flow , finite element method , convergence (economics) , solver , mathematics , shallow water equations , riemann solver , limit (mathematics) , flow (mathematics) , riemann problem , mathematical analysis , riemann hypothesis , geometry , mathematical optimization , mechanics , finite volume method , physics , engineering , structural engineering , economics , economic growth
Abstract 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 NC 1 − P NC 1 ), is presented, giving optimal rates of convergence in all test cases. P NC 1 − P 1 and P DG 1 − P 1 mixed formulations lack convergence for inviscid flows. P DG 1 − P 2 pair is more expensive but provides accurate results for all benchmarks. P DG 1 − P DG 1provides an efficient option, except for inviscid Coriolis‐dominated flows, where a small lack of convergence is observed. Copyright © 2009 John Wiley & Sons, Ltd.