SCAIM Seminar: Randall J. LeVeque

I will give a brief introduction to high-resolution (shock-capturing) finite volume methods for hyperbolic PDEs that model wave propagation. These methods are based on solving Riemann problems at cell interfaces and using wave limiters to develop second-order accurate methods that avoid non-physical oscillations around discontinuities in the solution. Riemann solver methods are also well adapted to problems of wave propagation in heterogeneous media with discontinuities in the material parameters. The Clawpack (Conservation Laws Package) software package implements these algorithms along with adaptive mesh refinement. I will give an overview of some of the recent developments in this project, including extensions to higher-order methods and to supercomputers through the PyClaw project. More about this open source software can be found at www.clawpack.org.