Parallel adaptive finite element methods for problems in natural convection

Numerical simulations of combined buoyant and surface tension driven flow, also known as Rayleigh-Bénard-Marangoni (RBM) convection are conducted for heated fluid layers of small aspect ratio (defined as the ratio of the horizontal extent of the domain divided by the depth of the fluid) in square cross-section containers. A particular non-dimensionalization of the governing equations is developed in which the aspect ratio of the domain appears as a continuous parameter. The simulations extend and enhance existing experimental studies of the RBM convection phenomenon by mapping continuous solution branches in aspect ratio and Marangoni number parameter space. Key implementation aspects of the development of the adaptive mesh refinement (AMR) library libMesh are discussed, and a series of simulations of the RBM problem with a stick-slip boundary condition demonstrate the suitability of AMR for computing these flows.