Multidimensional Flux-Vector-Splitting and High-Resolution Characteristic Schemes
Since the work of Godunov, Van Leer, Harten-Lax and Roe, the numerical solution of systems of hyperbolic conservation laws is dominated by Riemann-solver based schemes. These one-dimensional schemes are usually extended to several space-dimensions either by using dimensional-splitting on cartesian grids or by the finite-volume approach on unstructured grids. The first systematic criticism of using one-dimensional Riemann-solvers for multi-dimensional gas-dynamics goes back to Roe himself: the Riemann-solver is applied in the grid- rather than the flow-direction, which may lead to a misinterpretation of the local wave-structure of the solution.
KeywordsCartesian Grid Sonic Point Characteristic Scheme Linear Advection Equation Flux Vector Splitting
Unable to display preview. Download preview PDF.
- Fey M, Jeltsch R, Maurer J and Morel AT (1997). The method of transport for nonlinear systems of hyperbolic conservation laws in several space dimensions. Research Report No.97-12, Seminar for Applied Mathematics, ETH Zürich. Google Scholar
- Lukacova-Medvidova M, Morton K and Warnecke G (1997). Evolution Galerkin methods for hyperbolic systems in two space dimensions. Report 97-44, Univ. Magdeburg, GermanyTo appear inMath. Comp., 2000. Google Scholar
- Morel AT (1997). A genuinely multidimensional high-resolution scheme for the shallow-water equations. Dissertation, ETH Zürich Diss. No. 11959. Google Scholar
- Noelle S (1999). The MoT-ICE: a new high-resolution wave-propagation algorithm based on Fey’s Method of Transport. Invited plenary lecture. “Proceedings of the Second International Symposium on Finite Volumes for Complex Applications - Problems and Perspectives”, Duisburg, Germany, p. 95. For details see Preprint no. 1999-028 at http://www.math.ntnu.no/conservation/1999/028.html.Google Scholar