8:30 AM - 9:15 AM
Room: Town & Country
Chair:
Marsha Berger, Courant Institute of Mathematical Sciences, New York University
Many geophysical flows over topography can be modeled by two-dimensional depth-averaged fluid dynamics equations. The shallow water equations are the simplest example of this type, but it is often necessary to incorporate non-hydrostatic pressures, more complicated rheologies (e.g. for avalanches, landslides, or debris flows), or to use multi-layer models, e.g. for capturing internal waves or to model a landslide-induced tsunamis.
These models are generally hyperbolic and can be modeled using high-resolution finite volume methods designed for such problems. However, several features of these flows lead to new algorithmic challenges, such as the fact that the depth goes to zero at the edge of the flow and that vastly differing spatial scales must often be modeled, making adaptive mesh refinement essential. I will discuss some of these applications and the GeoClaw software, a specialized version of Clawpack that is aimed at solving real-world geophysical flow problems over topography.
Randall J. LeVeque
University of Washington