A stabilized finite element technique for transport phenomena within and around immersed porous bodies in flow

Mass transport in and around porous objects immersed in fluid flow is prevalent in a wide range of industrial and biomedical applications. These include medical devices, drug delivery, membrane-based processes, and pathophysiology of various disease scenarios, such as thrombosis. Numerical modeling using techniques, such as finite element method, is an important avenue for quantitative analysis of such transport processes. However, the presence of large discontinuities in concentrations, driven by discontinuous diffusivity and porosity, can lead to spurious numerical oscillations in finite element solutions. Here, we adopt a numerically consistent jump-stabilized finite element formulation, coupled with immersed non-conforming discretizations of the porous domain, to mitigate such spurious oscillatory behavior. We demonstrate that the resulting stabilized numerical method is robust in the pure advection (hyperbolic) and the pure diffusion (parabolic) limits of the transport equation. The stabilization contribution includes a tunable diffusion contribution to the system, ensuring that the solution does not become over-diffused. Subsequently, we present a series of illustrative simulation case studies, to show that the resulting stabilized algorithm can model transport processes in two- and three-dimensional settings, involving high spatial heterogeneity in porosity and highly arbitrary porous domain geometries that can vary non-trivially in space and time.