Abstract:

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, and are often sufficiently accurate for simulating tsunamis and other large-scale flows such as storm surge. Landslides and debris flows can also be modeled with depth-averaged equations by incorporating more complex rheology.

These hyperbolic partial differential equations can be modeled using high-resolution finite volume methods. However, several features of these flows lead to new algorithmic challenges, e.g. the need for well-balanced methods to capture small perturbations to the ocean at rest, the desire to model inundation and flooding, and that vastly differing spatial scales that must often be modeled, making adaptive mesh refinement essential. I will discuss some of the algorithms implemented in the open source software GeoClaw that is aimed at solving real-world geophysical flow problems over topography. I'll also show results of some recent studies of the 11 March 2011 Tohoku Tsunami and discuss the use of tsunami modeling in probabilistic hazard assessment.