Multidimensional schemes for nonlinear systems of hyperbolic conservation laws
Open access
Date
1995-11Type
- Report
ETH Bibliography
yes
Altmetrics
Abstract
Most commonly used schemes for unsteady multidimensional systems of hyperbolic conservation laws use dimensional splitting. In each coordinate direction a scheme for a one dimensional system is used. Such an approach does not take in account the infinitely many propagation directions which are present in a system in several space dimensions. In 1992 M. Fey introduced what he called the Method of Transport, MoT, for the Euler equations of gas dynamics. It is a finite volume method which uses the transport along characteristics. It does not compute fluxes across cellsides but from one cell to another. These type of schemes can be developed by first rewriting the Euler equation as a sum with integrals of infinitely many transport equations. One of these terms is related to the transport by the velocity while the integrals reflect the acoustic waves. In the numerical scheme the integrals are replaced by finite sums. The method can be modified such as to become a second order scheme. The technique can be applied to the magneto-hydrodynamic equations and the shallow water equation. Numerical examples for the shallow water equation are given. Show more
Permanent link
https://doi.org/10.3929/ethz-a-004284424Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
nonlinear hyperbolic conservation laws; multi-dimensional schemes; method of transport; second order; Euler equations of gas dynamics; shallow water equation; magneto-hydrodynamic equationsOrganisational unit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
More
Show all metadata
ETH Bibliography
yes
Altmetrics