Preconditioned conjugate gradients for solving the transient Boussinesq equations in three-dimensional geometries

0271-2091

Finite elements ; Transient flow ; Three-dimensional flow ; Natural convection ; Incomplete ; Choleski conjugate gradients ; Iterative solver ; Vectorization ; Crystal growth ; Gallium arsenide ; Engineering ; Engineering General

Wiley InterScience Backfile Collection 1832-2000

Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

In this paper we present a new version of the ‘modified finite element method’ (MFEM) presented by Gresho, Chan, Lee and Upson.1 The main modification of the original algorithm is the introduction of a cost-effective and memory-saving iterative solver for the discretized Poisson equation for the pressure. The vectorization of the preconditioner has been especially considered. For low Prandtl number problems we also split the advection-diffusion operator of the energy equation into explicit and implicit parts. In that sense the present approach is related to the recent implicitization of the diffusive terms introduced by Gresho and Chan2 and by Gresho.3 The algorithm is applied to the study of buoyancy-driven flow oscillations occuring in a horizontal crucible of molten metal under the action of a horizontal temperature gradient.

18 Ill.

Electronic Resource