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Improvements in mass conservation using alternative boundary implementations for a quasi‐bubble finite element shallow water model
Author(s) -
Bunya Shintaro,
Yoshimura Shinobu,
Westerink Joannes J.
Publication year - 2006
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.1153
Subject(s) - conservation law , conservation of mass , robustness (evolution) , finite element method , implementation , boundary value problem , bubble , boundary (topology) , shallow water equations , dirichlet boundary condition , local property , mathematical optimization , mathematics , computer science , mathematical analysis , engineering , mechanics , physics , structural engineering , biochemistry , chemistry , parallel computing , pure mathematics , gene , programming language
Finite element approaches generally do not guarantee exact satisfaction of conservation laws especially when Dirichlet‐type boundary conditions are imposed. This article discusses improvement of the global mass conservation property of quasi‐bubble finite element solutions for the shallow water equations, focusing on implementations of the surface‐elevation boundary conditions. We propose two alternative implementations, which are shown by numerical verification to be effective in improving the smoothness of solutions near the boundary and in reducing the mass conservation error. The improvement of the mass conservation property contributes to augmenting the reliability and robustness of long‐term time integrations. Copyright © 2006 John Wiley & Sons, Ltd.