Simulation of 3D flow in porous media by boundary element method

In the present paper problem of natural convection in a cubic porous cavity is studied numerically, using an algorithm based on a combination of single domain and subdomain boundary element method (BEM). The modified Navier–Stokes equations (Brinkman-extended Darcy formulation with inertial term included) were adopted to model fluid flow in porous media, coupled with the energy equation using the Boussinesq approximation. The governing equations are transformed by the velocity–vorticity variables formulation which separates the computation scheme into kinematic and kinetic parts. The kinematics equation, vorticity transport equation and energy equation are solved by the subdomain BEM, while the boundary vorticity values, needed as a boundary conditions for the vorticity transport equation, are calculated by single domain BEM solution of the kinematics equation. Computations are performed for steady state cases, for a range of Darcy numbers from 10−6 to 10−1, and porous Rayleigh numbers ranging from 50 to 1000. The heat flux through the cavity and the flow fields are analyzed for different cases of governing parameters and compared to the results in some published studies.

► Boundary element method is efficient for solving 3D flow problems in porous media.
► Brinkman viscous term becomes significant when Da   values are high (Da>10−4Da>10−4).
► Flow field in porous enclosure driven by a temperature difference is not far from being 2D.
► Three-dimensional motion in porous media is influenced mainly by values of Da and Rap.