Numerical simulation of incompressible flow driven by density variations during phase change

A change in density during the solidification of alloys can be an important driving force for convection, especially at reduced levels of gravity. A model is presented that accounts for shrinkage during the directional solidification of dendritic binary alloys under the assumption that the densities of the liquid and solid phases are different but constant. This leads to a non-homogeneous mass conservation equation, which is numerically treated in a finite element formulation with a variable penalty coefficient that can resolve the velocity field correctly in the all-liquid region and in the mushy zone. The stability of the flow when shrinkage interacts with buoyancy flows at low gravity is examined.