Conservative Schemes for Variable Coefficient Transport Equations
SIAM Annual Meeting 2018, Society for Industrial and Applied Mathematics, Portland, OR (USA) (Mini-symposium speaker) Jul 09 - Jul 01, 2018
We discuss at least four different methods for formulating the wave propagation algorithm used in Clawpack (R. J. LeVeque) for the variable coefficient conservative advection equation on a finite volume mesh. Both cell-centered and face-centered velocities are considered, and first and second order schemes. Of special interest is the treatment of sonic points where converging or diverging flows can lead to loss of hyperbolicity. We demonstrate the approaches on volcanic ash transport simulations, and if time permits, we discuss the correction terms needed to maintain conservation on adaptive mapped grids and surface meshes.