Christina Helzel
Universität Bonn
A high-resolution rotated grid method for the approximation of conservation laws in complex geometries
Abstract: We consider the approximation of multidimensional systems of conservation laws on Cartesian grids with embedded irregular boundaries. Our aim is to obtain a stable and accurate approximation with explicit finite volume methods using time steps that are appropriate for the regular grid cells. Grid cells near the boundary may be orders of magnitude smaller than a regular grid cell. Our approach is based on the so-called h-box method of Berger and LeVeque. This Godunov-type method calculates fluxes at cell interfaces by solving Riemann problems defined over boxes of a reference grid cell length h, i.e. the length of a regular grid cell. The accuracy of an h-box method depends strongly on the definition of the h-box values. We present and analyze a new second order accurate h-box method for the approximation of conservation laws on one-dimensional irregular grids. Insight obtained from this test problem is used to construct a high-resolution rotated grid method that can handle embedded boundaries in two-dimensional calculations. This is joint work with Marsha Berger and Randy LeVeque.| Zeit: | Friday, April 25, 2003, 16.00 Uhr |
| Ort: | FU Berlin, Arnimallee 2-6, Raum 032 im EG |