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Flux difference splitting for open‐channel flows
Author(s) -
Glaister P.
Publication year - 1993
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.1650160706
Subject(s) - flux limiter , mathematics , riemann problem , scalar (mathematics) , upwind scheme , riemann solver , shallow water equations , open channel flow , finite difference , limiter , supercritical flow , flow (mathematics) , finite difference method , roe solver , mathematical analysis , mechanics , finite volume method , geometry , riemann hypothesis , physics , computer science , telecommunications , discretization
A finite difference scheme based on flux difference splitting is presented for the solution of the one‐dimensional shallow‐water equations in open channels, together with an extension to two‐dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second‐order scheme which avoids non‐physical, spurious oscillations. The scheme is applied to a one‐dimensional dam‐break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two‐dimensional dam‐break problem. The numerical results are compared with the exact solution, or other numerical results, where available.