An analytical and numerical study of the Stefan problem with convection by means of an enthalpy method

In this paper, we consider a theoretical and numerical study of the Stefan problem with convection, described by the Navier–Stokes equations with no‐slip boundary conditions. The mathematical formulation adopted is based on the enthalpy method. The existence of a weak solution is proved in the bidimensional case. The numerical effectiveness of the model considered is confirmed by some numerical results. Copyright © 2001 John Wiley & Sons, Ltd.