Método Tangente Combinado para la Solución de Sistemas Altamente no Lineales Originados en Problemas de Cambio de Fase

Abstract

This paper presents a study of the solution procedure for phasechange problems. The heat transfer equation is discretized using finite elements and a fixed domain formulation. It is stressed the importance of an accurate evaluation of the residual vector. To do this we resort
to discontinuous integration in the phase-change elements. The solution of the nonlinear system of equation arising in this type of problems is achieved using an adequate modification of the Newton's method. The true tangent matrix proposed by the authors is used when the initial solution is in an adequately small neighborhood of the solution. Otherwise a consistent modification of this matrix is developed to enforce convergence when the initial solution is not near the solution. The numerial experiments show that the proprosed method has enhanced behaviour compared
to classical procedures.