Calculation of pressure in a mushy zone

The di$culties associated with the correct approximation of the pressure in numerical simulations of directional solidi"cation are examined. The suitability of methods available to calculate pressure in the presence of a mushy zone where #ow induced by density di!erences due to change of phase, or &shrinkageʹ, occurs is discussed, and a viable method of calculation based on the penalty function formulation is proposed. Results of calculations for #ows under reduced and normal gravity environments are presented