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A new enriched finite element formulation for solving isothermal phase change problems is presented. The proposed method is a fixed domain one, where the discontinuity in the temperature gradient is represented by means of enriching the finite element space through a function whose definition admits a discontinuity in its derivative. Generally, in this kind of formulations, the location where to enrich (as the location of the solidification front), is deter- mined through a level set auxiliary formulation. In this work a different approach is explored, this position is determined implicitly through a constraint that imposes that the temperature attained at the phase change boundary is the melting temperature. Some numerical examples to show the application of the method are presented and finally the conclusions are exposed.

TEMPERATURE GRADIENT DISCONTINUITY AWARE NUMERICAL SCHEME FOR SOLIDIFICATION PROBLEMS