Numerical solution of compressible fluid flow in porous media with boundary element method

In the present work a fully developed boundary element method numerical scheme is presented for the simulation of compressible fluid flow in porous media with restriction to the subsonic flows. The flow is modeled by utilizing the Brinkman extended Darcy momentum equation which is commonly used when it is important to satisfy the non-slip boundary condition on impermeable surfaces that bound the porous media domain. The governing equations are transformed by using the velocity-vorticity variables formulation and therefore the computation scheme is partitioned into kinematic and kinetic part. The method is applied to consider buoyancy driven flow in closed porous cavity, differentially heated under large temperature gradients. The results in terms of velocity and temperature redistribution as well as the total heat transfer across the cavity will be presented for different governing parameters.