Abstract:
High order numerical methods are formulated and analyzed for solving
multiphysics problems.
First, we consider discontinuous Galerkin methods of the incompressible
two-phase flow problem. In particular, adaptive simulations of a
sequential approach are shown. We also investigate a fully coupled
approach: error estimates are derived and numerical convergence in both
the mesh size and the polynomial degree are shown. One advantage of the
coupled approach is that no slope limiters are needed.
Second, we investigate the coupling of surface flow with subsurface
flow. Surface flow is characterized either by Navier-Stokes
equations whereas subsurface flow is characterized by Darcy equations.
Interface conditions include the continuity of the normal component of
the velocity, the balance of forces across the interface and the
Beaver-Joseph-Saffman condition.
We formulate two weak problems by considering two different interface
conditions for the balance of forces. We compare the two models and
show numerical examples.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.