Unstructuredmesh Solvers for Hyperbolic Pdes with Source Terms: Error Estimates and Mesh Quality

The solution of hyperbolic systems with sti source terms is of great importance in areas such as atmospheric dispersion. The nite-volume approach used here for such problems employs Godunov-type methods, a sophisticated splitting approach for e ciency and adaptive tetrahedral meshes to provide the necessary resolution for physically meaningful solutions. This raises the issues of how to estimate the error for Godunov type methods and what is an appropriate mesh for such applications. A new mesh visualization and haptic-interface tool will be shown to help clarify this and its use illustrated for a model problem in three space dimensions.