Note: Different Date and Location
Abstract:
Coupled Stokes and Darcy flows occur in a number of science and engineering
applications, including ground water - surface water interactions, flows
through fractured porous media, flows through vuggy rocks, and flows through
industrial filters. We discuss mathematical and numerical models for
chemical transport in Stokes-Darcy flow systems. Beavers-Joseph-Saffman
conditions are imposed on interfaces between Stokes and Darcy regions. We
prove existence and uniqueness of a weak flow solution. Stability and error
estimates are established for a finite element discretization based on
conforming or discontinuous elements for Stokes flow, mixed finite elements
for Darcy flow, and local discontinuous Galerkin elements for transport. The
formulation utilizes a Lagrange multiplier to impose the interface
conditions. A non-overlapping domain decomposition algorithm is developed
for the flow equations which reduces the coupled algebraic system to an
interface problem for the normal stress. Each interface iteration involves
solving Stokes and Darcy subdomain problems in parallel. The properties of
the interface operator are analyzed. Numerical results are presented.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.