Riemann Sweepers

Overview

We develop adaptive Cartesian mesh codes for nonlinear hyperbolic conservation laws. Our underlying algorithms are based on explicit, second order finite volume schemes for logically Cartesian meshes, and are implemented in the software package ClawPack, originally developed by R. J. LeVeque (Univ. of Washington). The main computational kernel of these Godunov-type schemes is a Riemann solver, written in a form that handles both conservative and nonconservative terms in a unified manner. Codes and packages in the ClawPack ecosystem are widely used for a variety of linear and nonlinear hyperbolic problems in two and three dimensions, including acoustics, gas dynamics, shallow water wave equations, advection, Burgers equation, elasticity and so on. The GeoClaw submodule, an application based on depth-averaged equations for geophysical flows, has been widely used to model tsunamis, landslides, storm surges, flooding, debris flows, and so on. Three dimensional ClawPack applications are currently being used for earthquake modeling (AMRClaw) and volcanic ash transport (ForestClaw).

Final presentation