Galerkin finite element simulation of convection driven by rotation and gravitation

The performance of the Galerkin finite element method when applied to time‐dependent convection involving rotation, self‐gravitation and the normal gravity field in a horizontal cylinder is discussed in this paper. The governing equations, the parameters of the problem and our implementation of the numerical schemes are presented. The accuracy, spatial scale of resolution, flexibility and robustness of the resulting code show the element method as a valuable tool for research in this area or in related problems in astrophysical fluid dynamics. The numerical difficulties in large‐amplitude flows are associated with an error‐control scheme for time integration and the ‘short‐time’ wiggles in transient Dirichlet problems. Coarse grids give the correct qualitative picture in most simulations, but the type of solution at short time (and hence grid refinement) presumably resolves the degeneracy in the azimuthal orientation of convection cells in flows driven by self‐gravitation and (perhaps) centrifugal buoyancy. The final state in transient flows is a motionless isothermal fluid. However, residual motions can be nullified only in the limit of zero grid size in flows driven by centrifugal buoyancy (self‐gravitation), while a fairly coarse grid is sufficient for this purpose in normal gravity‐driven flows.