A new numerical technique has been developed for the analysis of two‐dimensional transient solidification processes in the presence of time‐dependent natural convection in the melt. The method can cope with irregular, transient morphologies of the solid—liquid interface using a new Galerkin formulation for the energy balance on the solid—liquid interface. The finite element solution to the Galerkin formulation yields the displacement of individual nodes on the solid—liquid interface. The displacement of the nodes is expressed by uncoupled components in the x and y directions. The fluid flow problem was solved using a ‘penalty’ formulation. Numerical experiments were performed for Rayleigh numbers as high as 10 6 to demonstrate the method and to indicate the effect of natural convection on the solid—liquid interface morphology.
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Yoo et al. (1986) studied this question.
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