A temperature‐based finite element solution for phase‐change problems

Published in Int. J. Numer. Meth. Engng. Vol. 23 (1), pp. 99-119, 1986
doi: 10.1002/nme.1620230109

Abstract

A finite element procedure for solving multidimensional phase change problems is described. The algorithm combines a temperature formulation with a finite element treatment of the differential equation and discontinuous integration within the two‐phase elements to avoid the necessity of regularization. A new criterion for the computation of the iteration matrix is proposed. It is based on a quasi‐Newton correction of the Jacobian matrix for conduction problems without change of phase. A set of test problems with exact solution is analysed and demonstrates that the procedure can accurately evaluate the front position and temperature history with a reasonable computational effort.