CSE Symposium Keynote
DATE: Friday, April 28, 2000
TIME: 3:00 P.M.
PLACE: Second Floor Commons, Grainger Engineering Library
TITLE: Finite-Volume Methods and Software for Hyperbolic PDEs
and Conservation Laws
ABSTRACT
Hyperbolic systems of partial differential equations frequently arise
when modeling phenomena involving wave propagation or advective flow.
Finite-volume methods are a natural approach for conservation laws since
they are based directly on integral formulations and are applicable to
problems involving shock waves and other discontinuities. High-resolution
shock-capturing methods developed originally for compressible gas
dynamics can also be applied to other hyperbolic systems, even if not in
conservation form. I will describe a robust class of wave-propagation
methods that have been implemented in the CLAWPACK (Conservation
LAW PACKage) software for solving hyperbolic problems in one, two,
and three space dimensions. Adaptive mesh refinement capabilities are
also included. This software has been applied to a variety of problems
in diverse fields, including nonlinear elasticity, porous media flow,
geophysical flows on the sphere, combustion, waves in random media,
crystal growth, biological flows, and numerical relativity. Several
illustrative examples will be presented in the process of describing
these methods.