ADVANCED POROSITY CALCULATIONS papers

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Since the coupled Darcy- and mass-conservation equa-tions must normally be solved only in the mushy zone, it is necessary to introduce conditions at all the boundaries ofthis region. In previous articles dealing with microporosity formation, such computations were extended in the solidand liquid phases by using a penalty method, i.e., by setting a very small, respectively large, permeability.

However, asshown by Ampuero et al.,[6]special care has to be taken for the boundary condition imposed on the eutectic front grow-ing in between the dendrites in order to respect mass conser- vation and predict accurately the pressure field.In the present mushy-zone refinement technique, it is also essential to define appropriate boundary conditions at allthe boundaries. As illustrated in Figure 2, it is, therefore, necessary to first distinguish the nature of the remainingliquid regions that can be present in a casting. A region of liquid is a continuous portion of the solidifying domainwhere only the liquid phase is present. It can be one of the following.