Abstract A mathematical model which can describe flow and phase change of a number of phases at high temperatures is presented. It combines an interface capturing multiphase model, the P–1 radiation model, and a melting/solidification model. The resulting equations are solved by employing the finite volume discretization, a segregated solution procedure and the SIMPLE algorithm. The melting/solidification model is a finite rate model which in the limiting case behaves like a thermodynamic equilibrium model and it can also be used in situations where the phase change occurs within a range of temperatures as well as for problems where the phase change occurs at a constant temperature. The method is verified on a number of problems. The results obtained show a good agreement with exact solutions or results which can be found in literature.
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