- Howle, L.E., Efficient implementation of a finite-difference/Galerkin method for simulation of large aspect ratio convection,
Numerical Heat Transfer, Part B: Fundamentals, vol. 26 no. 1
pp. 105 - 114 .
(last updated on 2007/04/06)
The efficiency of a mixed finite-difference/Galerkin method is examined 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 summations 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 method extends to large-aspect-ratio problems that would previously be computationally impractical using the finite-difference/Galerkin technique.
Finite difference method;Tensors;Mathematical models;Boundary layers;Approximation theory;Function evaluation;Computational methods;