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Non‐oscillatory relaxation methods for the shallow‐water equations in one and two space dimensions
Author(s) -
Seaïd Mohammed
Publication year - 2004
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.766
Subject(s) - discretization , relaxation (psychology) , riemann hypothesis , shallow water equations , space (punctuation) , mathematics , riemann problem , waves and shallow water , mathematical analysis , computer science , physics , psychology , social psychology , thermodynamics , operating system
In this paper, a new family of high‐order relaxation methods is constructed. These methods combine general higher‐order reconstruction for spatial discretization and higher order implicit‐explicit schemes or TVD Runge–Kutta schemes for time integration of relaxing systems. The new methods retain all the attractive features of classical relaxation schemes such as neither Riemann solvers nor characteristic decomposition are needed. Numerical experiments with the shallow‐water equations in both one and two space dimensions on flat and non‐flat topography demonstrate the high resolution and the ability of our relaxation schemes to better resolve the solution in the presence of shocks and dry areas without using either Riemann solvers or front tracking techniques. Copyright © 2004 John Wiley & Sons, Ltd.