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Solution of shallow water equations using fully adaptive multiscale schemes
Author(s) -
Lamby Philipp,
Müller Siegfried,
Stiriba Youssef
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.1004
Subject(s) - shallow water equations , finite volume method , conservation law , hydraulic jump , wavelet , grid , mathematics , biorthogonal system , computer science , multiresolution analysis , oblique case , mathematical optimization , geometry , mathematical analysis , mechanics , flow (mathematics) , wavelet transform , physics , artificial intelligence , discrete wavelet transform , linguistics , philosophy
The concept of fully adaptive multiscale finite volume methods has been developed to increase spatial resolution and to reduce computational costs of numerical simulations. Here grid adaptation is performed by means of a multiscale analysis based on biorthogonal wavelets. In order to update the solution in time we use a local time stepping strategy that has been recently developed for hyperbolic conservation laws. The adaptive multiresolution scheme is now applied to two‐dimensional shallow water equations with source terms. The efficiency of the scheme is demonstrated on several problems with a general geometry, including circular damp breaks, oblique hydraulic jump, supercritical channel flows encountering sudden change in cross‐section, and, finally, the bore wave and its interactions. Copyright © 2005 John Wiley & Sons, Ltd.