An algorithm for solving unsteady incompressible viscous flows with free surface using a generalized coordinate system is proposed. In order to decide the free boundary configurations of the fluid, the extended VOF method is applied, and the enthalpy method extended to the generalized coordinate system is applied to consider the latent heat. The thermal resistance between two different materials is considered at the computational cell face. This algorithm is applied to the simulation of the molten metal flow with solidification in a belt and wheel type continuous casting. This calculation allows us to see the flow field with solidification in the mold cavity and the cooling effects of the mold.
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