Multiscale finite element modelling of flow through porous media with curved and contracting boundaries to evaluate different types of bubble functions

The Brinkman equation is used to model the isothermal flow of the Newtonian fluids through highly permeable porous media. Due to the multiscale behaviour of this flow regime the standard Galerkin finite element schemes for the Brinkman equation require excessive mesh refinement at least in the vicinity of domain walls to yield stable and accurate results. To avoid this, a multiscale finite element method is developed using bubble functions. It is shown that by using bubble enriched shape functions the standard Galerkin method can generate stable solutions without excessive near wall mesh refinements. In this paper the performances of different types of bubble functions are evaluated. These functions are used in conjunction with bilinear Lagrangian elements to solve the Brinkman equation via a penalty finite element scheme.