A moving grid numerical scheme for multi-dimensional solidification with transition temperature range Original Research Article

A numerical method is proposed to obtain temperatures and phase change boundaries in multi-dimensional solidification problems in which solidification takes place over a temperature range. Classical formulations have been considered for all the three – solid, liquid and mushy regions with thermodynamic equilibrium conditions and appropriate dynamic compatibility conditions at the solid–mush and liquid–mush boundaries. The numerical method uses the notion of moving grid points in conjunction with method of lines in space and employs finite difference discretization. Numerical results have been presented for two-dimensional solidification in a rectangular region. Axisymmetric cylindrical problems can also be considered and the method can be extended to three-dimensional solidification in a slab. Phase change boundaries can have curvatures. Accuracy of the numerical results has been accepted after satisfying several checks including an integral heat balance check.