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A well‐balanced upstream flux‐splitting finite‐volume scheme for shallow‐water flow simulations with irregular bed topography
Author(s) -
Lai JihnSung,
Guo WenDar,
Lin GwoFong,
Tan YihChi
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.2048
Subject(s) - finite volume method , hydrostatic equilibrium , benchmark (surveying) , upstream (networking) , mechanics , shallow water equations , stability (learning theory) , flow (mathematics) , coupling (piping) , scheme (mathematics) , computational fluid dynamics , mathematics , geometry , geology , computer science , physics , mathematical analysis , engineering , mechanical engineering , geodesy , quantum mechanics , machine learning , computer network
This study extends the upstream flux‐splitting finite‐volume (UFF) scheme to shallow water equations with source terms. Coupling the hydrostatic reconstruction method (HRM) with the UFF scheme achieves a resultant numerical scheme that adequately balances flux gradients and source terms. The proposed scheme is validated in three benchmark problems and applied to flood flows in the natural/irregular river with bridge pier obstructions. The results of the simulations are in satisfactory agreement with the available analytical solutions, experimental data and field measurements. Comparisons of the present results with those obtained by the surface gradient method (SGM) demonstrate the superior stability and higher accuracy of the HRM. The stability test results also show that the HRM requires less CPU time (up to 60%) than the SGM. The proposed well‐balanced UFF scheme is accurate, stable and efficient to solve flow problems involving irregular bed topography. Copyright © 2009 John Wiley & Sons, Ltd.