An efficient tangent scheme for solving phase-change problems

Published in Comput. Methods Appl. Mech. Engrg. Vol. 66(1), pp. 65-86, 1988
doi: 10.1016/0045-7825(88)90060-6

Abstract

Using weak formulations and finite elements to solve heat-conduction problems with phase change finally leads to the solution, at each time step, of a nonlinear system of equations in the nodal temperatures. The Newton-Raphson scheme is an effective procedure to cope with this type of problems; however, the choice of a good approximation to the tangent matrix is critical when the latent heat is comparatively large. In this work we derive an exact expression for the tangent matrix and analyze the behavior of its terms for different values of the physical parameters of the system. We demonstrate that this method has good convergence properties. In fact, the rate of convergence is quadratic when the trial approximation is sufficiently close to the solution. Finally, several numerical examples are given.