A numerical method for solving the two‐dimensional unsteady solidification problem with the motion of melt by using the boundary‐fitted co‐ordinate system

A numerical method for solving the two‐dimensional unsteady solidification problem with the motion of melt is proposed. The boundary‐fitted co‐ordinate system is applied to a treatment for the moving solid‐liquid interface in cylindrical co‐ordinates with a symmetry axis. An alternating‐direction‐implicit (ADI) method is used to solve the transformed equations of motion and energy, which are expressed in terms of the vorticity and stream function. Several examples are displayed.