Well-Balanced Adaptive Mesh Refinement for shallow water flows

Authors:
Rosa Donat;M. Carmen Martí;Anna Martínez-Gavara;Pep Mulet
Affiliations:
Departament de Matemítica Aplicada, Universitat de València, Spain;Departament de Matemítica Aplicada, Universitat de València, Spain;Departament de Estadística i Investigació Operativa, Universitat de València, Spain;Departament de Matemítica Aplicada, Universitat de València, Spain
Venue:
Journal of Computational Physics
Year:
2014

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Abstract

Well-balanced shock capturing (WBSC) schemes constitute nowadays the state of the art in the numerical simulation of shallow water flows. They allow to accurately represent discontinuous behavior, known to occur due to the non-linear hyperbolic nature of the shallow water system, and, at the same time, numerically maintain stationary solutions. In situations of practical interest, these schemes often need to be combined with some kind of adaptivity, in order to speed up computing times. In this paper we discuss what ingredients need to be modified in a block-structured AMR technique in order to ensure that, when combined with a WBSC scheme, the so-called 'water at rest' stationary solutions are exactly preserved.