Beatrice Riviere, University of Pittsburgh

Modeling complex flow and transport processes
 
In this talk, we present high order numerical methods for solving
multiphysics problems. First, we investigate the coupling of surface
flow with subsurface flow. Surface flow is characterized either by
Stokes or Navier-Stokes equations whereas subsurface flow is
characterized by Darcy equations.  Special interface conditions are
considered between the subregions.  Locally conservative methods, such
as discontinuous Galerkin or mixed finite element methods, are used.
Optimal error estimates are obtained.  Second, we consider both
implicit and explicit discontinuous formulations of the incompressible
two-phase flow problem.  In particular, we show numerical convergence
of the p-version.  An interesting fact is that no slope limiters are
needed for the implicit method.