EFFICIENT IMPLEMENTATION OF A FINITE-DIFFERENCE GALERKIN METHOD FOR SIMULATION OF LARGE ASPECT RATIO CONVECTION

The efficiency of a mixed finite-difference/Galerkin method is examine d for simulation of steady two-dimensional Rayleigh-Benard convection of large aspect ratio. It is found that computation time is reduced by an order of magnitude for large-aspect-ratio systems if the summation s resulting from the formation of inner products are expanded prior to code compilation. The expansion of the summations is carried out by a source code utility, which writes the expanded and simplified source. This eliminates the need to store and multiply sparse tensors. The me thod extends to large-aspect-ratio problems that would previously be c omputationally impractical using the finite-difference/Calerkin techni que.