Velocity–vorticity formulation for 3D natural convection in an inclined enclosure by BEM

A natural convection phenomenon is studied in cubic and parallelepipedal inclined enclosures. The simulation of coupled laminar viscous flow and heat transfer is performed using a novel algorithm based on a combination of single domain Boundary element method (BEM) and subdomain BEM. The algorithm solves the velocity–vorticity formulation of the incompressible Navier–Stokes equations coupled with the energy equation using the Boussinesq approximation. The subdomain BEM is used to solve the kinematics equation, the vorticity transport equation and the energy equation. The boundary vorticity values, which are needed as boundary conditions for the vorticity transport equation, are calculated by singe domain BEM solution of the kinematics equation. Simulation results are compared with benchmark results for a cubic inclined enclosure for Rayleigh number values 10 3 ⩽ Ra ⩽ 10 5 . The results for an inclined enclosure with width to height ratio 1:2 are also presented.