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 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 for dendritic growth of four dendrites.
Binary Alloy High Aspect Ratio Posteriori Error Dendritic Growth Liquid Region
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