Finite elements for well-reservoir coupling.
Juan Carlos Galvis
Inf -sup condition | Stokes-Darcy | Finite Elements.
We analyze the coupling across an interface of fluid and porous media flows. Some applications are: Coupling surface and groundwater water flow, well and oil reservoir and biofluid dynamics models (several organs can be viewed as a porous medium, organs like brain, heart, lung). We consider the Stokes equations in the fluid region and Darcy law for the filtration velocity in the porous medium. Beavers-Joseph conditions for the interface are considered. We use the porous pressure as a Lagrange multiplier to couple the model and develop inf-sup conditions at the continuous and discrete levels. Using the second order Taylor-Hood and the lowest Raviart-Thomas finite elements, optimal discrete approximations and inf-sup conditions based on constructing Fortin's interpolations are provided. Numerical experiments are presented.