246 RWTH Publication No: 47147        2004        IGPM246.pdf
TITLE Solution of Shallow Water Equations Using Fully Adaptive Multiscale Schemes
AUTHORS Philipp Lamby, Siegfried Müller, Youssef Stiriba
ABSTRACT 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.
KEYWORDS shallow water equations, multiscale techniques, local grid refinement, finite volume methods
DOI 10.1002/fld.1004
PUBLICATION International journal for numerical methods in fluids
49(4), 417-437 (2005)