Verlagslink DOI: 10.1002/zamm.200510280
Titel: Comparison study of some finite volume and finite element methods for the shallow water equations with bottom topography and friction terms
Sprache: Englisch
Autor/Autorin: Medviďová-Lukáčová, Mária
Teschke, Ulf
Schlagwörter: well-balanced schemes, steady states, systems of hyperbolic balance laws, shallow water equations, evolution Galerkin schemes
Erscheinungsdatum: 2005
Quellenangabe: Preprint. Published in: Z. angew. Math. Mech. (ZAMM), 86(11), 2006, 874–891
Serie/Report Nr.: Preprints des Institutes für Mathematik; Bericht 87
Zusammenfassung (englisch): We present a comparison of two discretization methods for the shallow water equations, namely the finite volume method and the finite element scheme. A reliable model for practical interests includes terms modelling the bottom topography as well as the friction effects. The resulting equations belong to the class of systems of hyperbolic partial differential equations of first order with zero order source terms, the so-called balance laws. In order to approximate correctly steady equilibrium states we need to derive a well-balanced approximation of the source term in the finite volume framework. As a result our finite volume method, a genuinely multidimensional finite volume evolution Galerkin (FVEG) scheme, approximates correctly steady states as well as their small perturbations (quasi-steady states). The second discretization scheme, which has been used for practical river flow simulations, is the finite element method (FEM). In contrary to the FVEG scheme, which is a time explicit scheme, the FEM uses an implicite time discretization and the Newton-Raphson iterative scheme for inner iterations. We compare the accuracy and performance of both scheme through several numerical experiments, which demonstrate the reliability of both discretization techniques and correct approximation of quasisteady states with bottom topography and friction.
URN: urn:nbn:de:gbv:830-opus-1672
DOI: 10.15480/882.109
Institut: Mathematik E-10
Mathematics E-10
Dokumenttyp: Preprint (Vorabdruck)
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