Fast iterative solvers for buoyancy driven flow problems

We outline a new class of robust and efficient methods for solving the Navier–Stokes equations with a Boussinesq model for buoyancy driven flow. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams–Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the efficiency of the chosen preconditioning schemes with respect to the discretization parameters.