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Compatibility between finite volumes and finite elements using solutions of shallow water equations for substance transport
Author(s) -
Postma Leo,
Hervouet JeanMichel
Publication year - 2006
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.1373
Subject(s) - finite volume method , finite element method , shallow water equations , mathematics , hydraulics , compatibility (geochemistry) , extended finite element method , mathematical analysis , geology , mechanics , engineering , physics , thermodynamics , structural engineering , geochemistry
This paper formulates a finite volume analogue of a finite element schematization of three‐dimensional shallow water equations. The resulting finite volume schematization, when applied to the continuity equation, exactly reproduces the set of matrix equations that is obtained by the application of the corresponding finite element schematization to the continuity equation. The procedure allows the consistent and mass conserving coupling of the finite element Telemac model for three‐dimensional flow with the finite volume Delft3D‐WAQ model for water quality. The work has been carried out as part of a joint development by LNHE and WL∣Delft Hydraulics to explore the mutual interaction of their software. Copyright © 2006 John Wiley & Sons, Ltd.