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River and reservoir flow modelling using the transformed shallow water equations
Author(s) -
Borthwick A. G. L.,
Barber R. W.
Publication year - 1992
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.1650141005
Subject(s) - curvilinear coordinates , shallow water equations , waves and shallow water , flow (mathematics) , free surface , boundary value problem , geology , finite difference method , mathematics , mechanics , geometry , mathematical analysis , physics , oceanography
Abstract This paper describes a versatile finite difference scheme for the solution of the two‐dimensional shallow water equations on boundary‐fitted non‐orthogonal curvilinear meshes. It is believed that this is the first non‐orthogonal shallow water equation model incorporating the advective acceleration terms to have been developed in the United Kingdom. The numerical scheme has been validated against the severe condition of jet‐forced flow in a circular reservoir with vertical side walls, where reflections of the initial free surface waves pose major problems in achieving a stable solution. Furthermore, the validation exercises are designed to test the computer model for artificial diffusion, which may be a consequence of the numerical scheme adopted to stabilize the shallow water equations. The model is shown to be capable of simulating the flow conditions in an irregularly shaped domain typical of the geometries frequently encountered in civil engineering river basin management.