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Practical evaluation of five partly-discontinuous finite element pairs for the non-conservative shallow water equations
Comblen, R.; Lambrechts, J.; Remacle, J.-F.; Legat, V. (2010). Practical evaluation of five partly-discontinuous finite element pairs for the non-conservative shallow water equations. Int. J. Numer. Methods Fluids 63(6): 701-724. hdl.handle.net/10.1002/fld.2094
In: International Journal for Numerical Methods in Fluids. Wiley Interscience: Chichester; New York. ISSN 0271-2091, more
Peer reviewed article  

Available in Authors 
    VLIZ: Open Repository 279731 [ OMA ]

Author keywords
    finite element; shallow water equations; discontinuous Galerkin; non-conforming element; Riemann solver; convergence

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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 (Pmath image-Pmath image), is presented, giving optimal rates of convergence in all test cases. Pmath image-P1 and Pmath image-P1 mixed formulations lack convergence for inviscid flows. Pmath image-P2 pair is more expensive but provides accurate results for all benchmarks. Pmath image-Pmath image provides an efficient option, except for inviscid Coriolis-dominated flows, where a small lack of convergence is observed.

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