Numerical solutions of the Stefan problem by the enthalpy method and the heat balance integral method

A novel enthalpy formulation is applied to the Stefan problem in various types of domains, including cylindrical and spherical geometries, annuli, and two-dimensional square domains. The results are compared with exact solutions; when exact solutions are unavailable, comparison is made between the enthalpy method and the heat balance integral method (HBIM), a front-tracking method that has been applied successfully in simple domains. The enthalpy formulation provides a simple way of tracking the phase front and is shown to be accurate even with relatively coarse grids.