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Discontinuous boundary implementation for the shallow water equations
Author(s) -
Bunya Shintaro,
Westerink Joannes J.,
Yoshimura Shinobu
Publication year - 2005
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.813
Subject(s) - discontinuity (linguistics) , boundary (topology) , boundary value problem , momentum (technical analysis) , shallow water equations , mathematics , boundary conditions in cfd , advection , instability , bubble , singular boundary method , elevation (ballistics) , boundary element method , mathematical analysis , boundary knot method , neumann boundary condition , finite element method , robin boundary condition , mechanics , geometry , physics , finance , economics , thermodynamics
Quasi‐bubble finite element approximations to the shallow water equations are investigated focusing on implementations of the surface elevation boundary condition. We first demonstrate by numerical results that the conventional implementation of the boundary condition degrades the accuracy of the velocity solution. It is also shown that the degraded velocity leads to a critical instability if the advection term is present in the momentum equation. Then we propose an alternative implementation for the boundary condition. We refer to this alternative implementation as a discontinuous boundary (DB) implementation because it introduces at each boundary node two independent mass–flux values that result in a discontinuity at the boundary. Numerical results show that the proposed DB implementation is consistent, stabilizes the quasi‐bubble scheme, and leads to second‐order accuracy at the surface elevation specified boundary. Copyright © 2004 John Wiley & Sons, Ltd.