T31E-05
Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

Wednesday, 16 December 2015: 09:00
304 (Moscone South)
Nathan Collier, Oak Ridge National Laboratory, Oak Ridge, TN, United States and Matthew Knepley, Rice University, Houston, TX, United States
Abstract:
The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).