Unstructured finite element method for the solution of the Boussinesq problem in three dimensions

We present a numerical method for the monolithic discretisation of the Boussinesq system in three spatial dimensions. The key ingredients of the proposed methodology are the finite element discretisation of the spatial part of the problem using unstructured tetrahedral meshes, an implicit time integrator, based on adaptive predictor-corrector scheme (the explicit second-order Adams-Bashforth method with the implicit stabilised trapezoid rule), and a new preconditioned Krylov subspace solver for the resulting linearised discrete problem. We test the proposed methodology on a number of physically relevant cases, including laterally heated cavities and the Rayleigh-Bénard convection. © 2013 John Wiley & Sons, Ltd.