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An approximate‐state Riemann solver for the two‐dimensional shallow water equations with porosity
Author(s) -
FinaudGuyot P.,
Delenne C.,
Lhomme J.,
Guinot V.,
Llovel C.
Publication year - 2009
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2066
Subject(s) - riemann solver , shallow water equations , solver , riemann problem , rarefaction (ecology) , mathematics , conservation law , momentum (technical analysis) , porosity , computation , mathematical analysis , riemann surface , riemann hypothesis , mechanics , mathematical optimization , physics , geology , geotechnical engineering , finite volume method , algorithm , paleontology , finance , species richness , economics
PorAS, a new approximate‐state Riemann solver, is proposed for hyperbolic systems of conservation laws with source terms and porosity. The use of porosity enables a simple representation of urban floodplains by taking into account the global reduction in the exchange sections and storage. The introduction of the porosity coefficient induces modified expressions for the fluxes and source terms in the continuity and momentum equations. The solution is considered to be made of rarefaction waves and is determined using the Riemann invariants. To allow a direct computation of the flux through the computational cells interfaces, the Riemann invariants are expressed as functions of the flux vector. The application of the PorAS solver to the shallow water equations is presented and several computational examples are given for a comparison with the HLLC solver. Copyright © 2009 John Wiley & Sons, Ltd.