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International Conference on Mathematical Modeling and Scientific Computing
April 2-6, 2001
Middle East Technical University and Selcuk University
Ankara and Konya, Turkey

Organizers
F. Bornemann (Munich University of Tecnology, Germany), H. Bulgak (Selcuk University, Konya, Turkey), V. Ganzha (Munich University of Technology, Germany), B. Karasozen (METU, Ankara, Turkey), A. Sinan (Selcuk University, Konya, Turkey), C. Zenger (Munich University of Technology, Germany)

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Composite finite difference schemes for conservation laws
by
Richard Liska
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Check Republic

The basic idea of composite schemes is rather simple, they consist of several steps of a dispersive second order scheme and one step of diffusive scheme which serves as a consistent filter removing well-known dispersive oscillations behind the shocks. As dispersive schemes we use Lax-Wendroff (LW) type schemes while as diffusive schemes we use Lax-Friedrichs (LF) type schemes. We have done also some experiments with WENO hyperdiffusive scheme. We have found the composite schemes while experimenting with filters on 1D shallow water problems and it turned out that the composite schemes work well also in higher dimensions and for other systems of conservation laws including Euler equations. New versions of non-split two step LF and LW type schemes have been developed in 2D and 3D on orthogonal grids. The 2D schemes have been generalized to arbitrary logically rectangular grids and to unstructured meshes with triangular and staggered n-lateral grids.

http://www-troja.fjfi.cvut.cz/~liska

Date received: December 28, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagk-12.