An explicit stabilised finite element method for Navier-Stokes-Brinkman equations

We present an explicit stabilised finite element method for solving Navier-Stokes-Brinkman equations. The proposed algorithm has several advantages. First, the lower equal-order space velocity and pressure is ideal presenting pixel images. Stabilised allows continuity of both tangential normal velocities at interface between regions different micro-permeability or free/porous domain. Second, fully versatile describing complex boundary conditions. Third, matrix–free implementation parallelism on high-performance computers. In last, implicit treatment Darcy term allowed larger time stepping a stable computation, even if varies orders magnitude in micro-porous (Darcy regime). stabilisation parameter, that may affect field, been discussed optimal parameter was chosen based numerical examples. Velocity stability also studied with mesh refinement. analysed influence field regime flow (Stokes flow, transitional These benchmark tests provide guidelines choosing resolution grayscale image its segmentation. applied real Berea Sandstone micro-CT images, proceeded three-phases micro-porosity using well-known Kozeny-Carman relation to derive from effective permeability computed. Our analysis shows small fraction rock significant