In this work, the melting of a horizontal substrate placed beneath a heavier liquid is simulated numerically. A finite difference method is used to solve simultaneously the equations governing the conservation of mass, momentum and energy in the liquid-liquid layers. The equations for the two-phases are coupled through the matching of normal and tangential stresses and continuity of mass at the interface. A second-order projection method is employed for decoupling velocities from pressure. A numerical grid generation method is used to construct a grid system, which is aligned with the interface. The numerical results are compared with experimental data reported in the literature. (C) 1997 Elsevier Science Ltd.