Three-dimensional natural convection in a porous cavity by the boundary element method

摘要

A thee-dimensional numerical simulation of convective flow in porous media using an algorithm based on a combination of a single domain and a subdomain boundary element method (BEM) is presented. The fluid flow in porous media is modeled with the modified Navier-Stokes equations (Brinkman-extended Darcy formulation with inertial term included) coupled with the energy and species equations using the Boussinesq approximation. The velocity-vorticity formulation is adopted to solve the governing set of equations, which results in decoupling of the computational scheme into the kinematic and kinetic computational parts. The boundary vorticity values are calculated by a single domain BEM solution of the kinematics equation, while the subdomain BEM is used to solve the vorticity, energy and species transport equations. Computations are performed for various governing parameters (Rayleigh number, Darcy number, Lewis number, buoyancy coefficient) and, simulation results are compared to the results of some published studies. Heat and mass flux through the cavity and flow fields are analyzed, focusing on the 3D nature of the phenomena.