Plenary Session - Thursday, July 17, 9:00 am

I will describe a general class of finite volume methods for solving hyperbolic systems of partial differential equations. These equations often 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 many other hyperbolic systems, even if not in conservation form. The basic ingredient is a "Riemann solver" that resolves piecewise constant initial data into a set of propagating waves, together with limiter functions that yield high-resolution results without unphysical oscillations. This approach is useful for problems in heterogeneous media (with discontinuous material properties) as well as for problems with discontinuous solutions. The general wave-propagation formulation has been implemented in the CLAWPACK software package, which also includes adaptive mesh refinement in two and three space dimensions.
These methods are applicable to a wide variety of problems, including seismic wave propagation, soil liquifaction, porous media flow, shallow water flow in rivers and estuaries, tsunami propagation, and the dispersal of pollution or volcanic ash. Several illustrative examples will be presented in the process of describing these methods.

Bio
Randall J. LeVeque, Professor of Applied Mathematics at the University
of Washington, received his Ph.D. in Computer Science from Stanford
University in 1982. He has also held positions at the Courant Institute
(NYU), UCLA, and ETH-Zurich.

LeVeque's research primarily concerns numerical methods for solving
nonlinear partial differential equations arising in physical
applications, particularly computational fluid dynamics and wave
propagation problems. He is interested in the design of better
algorithms, their software implementation, and a variety of scientific and
engineering applications. LeVeque is the author of two books on numerical
methods for hyperbolic problems and currently serves as editor of the
Survey and Review secion of SIAM Review.

E-mail questions and inquiries to em03@ce.washington.edu.