Multiscale Finite Element Modelling of Flow Through Porous Media with Curved and Contracting Boundaries to Evaluate Different Types of Bubble Functions (Communications in Computational Physics, 2007)
The Brinkman equation is used to model the isothermal flow of the Newtonian fluids through highly permeable porous media. Due to the multiscale behaviourof this flow regime the standard Galerkin finite element schemes for the Brinkmanequation require excessive mesh refinement at least in the vicinity of domain walls toyield stable and accurate results. To avoid this, a multiscale finite element method isdeveloped using bubble functions. It is shown that by using bubble enriched shapefunctions the standard Galerkin method can generate stable solutions without excessive near wall mesh refinements. In this paper the performances of different types ofbubble functions are evaluated. These functions are used in conjunction with bilinear Lagrangian elements to solve the Brinkman equation via a penalty finite elementscheme.