In this talk, I will firstly introduce the theory of saddle point problems. Some numerical algorithms for a model of fluid flow interacting with porous media flow will be presented and justified. In particular, decoupled preconditioning techniques and a two grid algorithm for a coupled Stokes/Darcy model will be discussed in detail.
Some possible extensions of the algorithms for Multiphysics models including two phase flow model, fluid structure interaction model, and fluid poroelastic material interaction model will also be addressed.
This presentation is an expository talk. All researchers and students who are interested in PDE theory, numerical linear algebra, fluid dynamics, environmental sciences, geoscience, and biomechanics are very welcome.