期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 206, 期 1, 页码 311-333出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2004.12.016
关键词
Saint-Venant system; shallow water flow; finite volumes; kinetic solver; hydrostatic reconstruction; well-balanced scheme; positivity preserving scheme; second-order extension
We consider the solution of the Saint-Venant equations with topographic source terms on 2D unstructured meshes by a finite volume approach. We first present a stable and positivity preserving homogeneous solver issued from a kinetic representation of the hyperbolic conservation laws system. This water depth positivity property is important when dealing with wet-dry interfaces. Then, we introduce a local hydrostatic reconstruction that preserves the positivity properties of the homogeneous solver and leads to a well-balanced scheme satisfying the steady-state condition of still water. Finally, a formally second-order extension based on limited reconstructed values on both sides of each interface and on an enriched interpretation of the source terms satisfies the same properties and gives a noticeable accuracy improvement. Numerical examples on academic and real problems are presented. (c) 2005 Published by Elsevier Inc.
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