Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows

Authors:
Sebastian Noelle;Normann Pankratz;Gabriella Puppo;Jostein R. Natvig
Affiliations:
Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany;Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany;Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy;SINTEF ICT, Forskningsveien 1, N0314 Oslo, Norway
Venue:
Journal of Computational Physics
Year:
2006

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Abstract

Many geophysical flows are merely perturbations of some fundamental equilibrium state. If a numerical scheme shall capture such flows efficiently, it should be able to preserve the unperturbed equilibrium state at the discrete level. Here, we present a class of schemes of any desired order of accuracy which preserve the lake at rest perfectly. These schemes should have an impact for studying important classes of lake and ocean flows.