Edge stabilized finite element method for mass transport within and around an immersed porous media

Mass transport phenomena in immersed porous media is relevant for multiple engineering and biomedical applications. These problems can be characterized by a large spatial jump in flow, and mass transport coefficients along the interface between the free flowing and the immersed porous regions. Streamline upwind Petrov-Galerkin (SUPG) stabilized finite elements (FE) are very efficient in simulating mass transport problems at moderately high Peclet number. However, SUPG is known to still produce spurious oscillations at the location of sharp transport discontinuities without excessive mesh refinement. These oscillations ultimately pollute the solution and can be inadmissible in many applications. In problems where the immersed porous medium interface moves, adaptive mesh refinement can be computationally expensive. In this contribution, we propose the adoption of a linear edge stabilization FE technique to augment traditional SUPG stabilized FE methods to resolve instabilities at the porous medium interface. A series of model mass transport problems through porous media will be presented to evaluate the performance of the stabilization methodology. Finally, an example biological application of mass transport through a complex moving porous media will be demonstrated.