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Two‐dimensional shallow water equations by composite schemes
Author(s) -
Liska Richard,
Wendroff Burton
Publication year - 1999
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/(sici)1097-0363(19990630)30:4<461::aid-fld850>3.0.co;2-4
Subject(s) - shallow water equations , composite number , waves and shallow water , shock (circulatory) , supercritical flow , flow (mathematics) , dam break , mathematics , shock wave , scheme (mathematics) , mechanics , mathematical analysis , geology , geometry , physics , algorithm , medicine , philosophy , oceanography , theology , flood myth
Composite schemes are formed by global composition of several Lax–Wendroff steps followed by a diffusive Lax–Friedrichs or WENO step, which filters out the oscillations around shocks typical for the Lax–Wendroff scheme. These schemes are applied to the shallow water equations in two dimensions. The Lax–Friedrichs composite is also formulated for a trapezoidal mesh, which is necessary in several example problems. The suitability of the composite schemes for the shallow water equations is demonstrated on several examples, including the circular dam break problem, the shock focusing problem and supercritical channel flow problems. Copyright © 1999 John Wiley & Sons, Ltd.