ABSTRACT
This chapter discusses front-tracking methods and explains the most general and versatile method available for the numerical simulation of phase-change processes, the so-called enthalpy method. It presents the mathematical ideas underlying weak formulations of Partial Differential Equation (PDE) problems, and the mathematical formulation on which the enthalpy method is based. The chapter establishes existence of the weak solution and convergence of the enthalpy scheme to the weak solution. The only viable general approach is the so-called enthalpy method, precisely because it bypasses the explicit tracking of the interface. In this approach the jump condition is not forced on the solution, but it is obeyed automatically by it as a "natural boundary condition". The, so called, enthalpy or weak solution approach is based on the fact that the energy conservation law, expressed in terms of energy and temperature, together with the equation of state contain all the physical information needed to determine the evolution of the phases.
