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Friction term discretization and limitation to preserve stability and conservation in the 1D shallow‐water model: Application to unsteady irrigation and river flow
Author(s) -
Burguete J.,
GarcíaNavarro P.,
Murillo J.
Publication year - 2007
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.1727
Subject(s) - discretization , pointwise , shallow water equations , stability (learning theory) , term (time) , mechanics , mathematics , flow (mathematics) , momentum (technical analysis) , work (physics) , geotechnical engineering , mathematical analysis , geology , geometry , engineering , computer science , physics , mechanical engineering , finance , quantum mechanics , machine learning , economics
Friction is one of the relevant forces included in the momentum equation of the 1D shallow‐water model. This work shows that a pointwise discretization of the friction term unbalances this term with the rest of the terms in the equation in steady state. On the other hand, an upwind discretization of the friction term ensures the correct discrete balance. Furthermore, a conservative technique based on the limitation of the friction value is proposed in order to avoid unbounded values of the friction term in unsteady cases of advancing front over dry and rough surfaces. This limitation improves the quality of unsteady solutions in wet/dry fronts and guarantees the numerical stability in cases with dominant friction terms. The proposed discretization is validated in some test cases with analytical solution or with measured data and used in some practical cases. Copyright © 2007 John Wiley & Sons, Ltd.