Solution of the moving-boundaries problems

In the present study, a new method for solving the moving-boundaries problems is presented. The focus of our analysis of this technique is the mathematical formulation of the basic physical facts leading to the solid-liquid phase change. At each lime step, the main idea is first to compute the solution without accounting for the discontinuity at the moving boundary; then, an exact local equation, which we call the Moknine relation, is used to produce the solution accounting for the discontinuity. Thus, no nonlinearity due to the apriori unknown interface position and no problem of missing the phase change are encountered when the solution is produced. This technique does not depend on the geometry considered or the nonlinearity due to the variation of Be thermophysical data. Finally, the methodology is applied in the case of a one-dimensional problem. The numerical results for the phase change at a single point thus obtained are compared with the Newman solution.