Adaptive finite elements with high aspect ratio for dendritic growth of a binary alloy including fluid flow induced by shrinkage

An adaptive phase field model for the solidification of binary alloys in two space dimensions is presented. The fluid flow in the liquid due to different liquid/solid densities is taken into account. The unknowns are the phase field, the alloy concentration and the velocity/pressure in the liquid.Continuous, piecewise linear finite elements are used for the space discretization, a semi-implicit scheme is used for the time discretization. An adaptive method allows the number of degrees of freedom to be reduced, the mesh triangles having high aspect ratio whenever needed.Numerical results are presented, showing that the fluid flow due to different liquid/solid densities must be taken into account. Moreover, numerical experiments pertaining to micro-porosity and hot tearing are reported.