A two-phase enthalpy method

A "compact" finite difference scheme to solve two-phase Stefan problems in one-dimension is described. This type of scheme was proposed by Milton E. Rose for the one-phase problem. Integration over control volumes and backward and forward differences are used to develop an enthalpy scheme that converges to the weak solution of the two-phase Stefan problem. Numerical results are compared to the exact Neumann (similarity) solution and to numerical solutions from an explicit and an SOR enthalpy scheme.