An EBE finite element method for simulating nonlinear flows in rotating spheroidal cavities

Many planetary and astrophysical bodies are rotating rapidly, fluidic and, as a consequence of rapid rotation, in the shape of an ablate spheroid. We present an efficient element-by-element (EBE) finite element method for the numerical simulation of nonlinear flows in rotating incompressible fluids that are confined in an ablate spheroidal cavity with arbitrary eccentricity. Our focus is placed on temporal and spatial tetrahedral discretization of the EBE finite element method in spheroidal geometry, the EBE parallelization scheme and the validation of the nonlinear spheroidal code via both the constructed exact nonlinear solution and the special resonant forcing in the inviscid limit. Copyright (C) 2009 John Wiley & Sons, Ltd.