H. Hu and S. A. Argyropoulos, Mathematical modelling of solidification and melting: a review, Modelling and Simulation in Materials Science and Engineering, vol.4, issue.4, pp.371-396, 1996.

V. R. Voller, An overview of numerical methods for solving phase change 490 problems, Advances in numerical heat transfer, vol.1, issue.9, pp.341-380, 1997.

E. Assis, L. Katsman, G. Ziskind, and R. Letan, Numerical and experimental study of melting in a spherical shell, International Journal of Heat and Mass Transfer, vol.50, issue.9, pp.1790-1804, 2007.

S. Wang, A. Faghri, and B. T. , A comprehensive numerical model for melting with natural convection, International Journal of Heat and Mass Transfer, vol.53, pp.1986-2000, 2010.

C. An and J. Su, Lumped parameter model for one-dimensional melting in a slab with volumetric heat generation, Applied Thermal Engineering, vol.60, issue.1, pp.387-396, 2013.

J. Crepeau and A. Siahpush, Approximate solutions to the Stefan problem with internal heat generation, Heat and Mass Transfer, vol.44, issue.7, pp.787-794, 2008.

J. C. Crepeau, A. Siahpush, and B. Spotten, On the Stefan problem with volu-505 metric energy generation, Heat and Mass Transfer, vol.46, issue.1, pp.119-128, 2009.

J. M. Bonnet and J. M. Seiler, Thermohydraulic phenomena in corium pool: the bali experiment, 1999.

R. L. Tellier, L. Saas, and F. Payot, Phenomenological analyses of corium prop-510 agation in LWRs: the PROCOR software platform, in: Proc. of the 7th

, European Review Meeting on Severe Accident Research ERMSAR, 2015.

G. Carey, Derivative calculation from finite element solutions, Computer Methods in Applied Mechanics and Engineering, vol.35, pp.1-14, 1982.

. Fauske-&-associates-inc, MAAP4 -modular accident analysis program for LWR power plants, Code Structure and Theory, vol.2, 1994.

G. M. Phillips, Explicit forms for certain hermite approximations, BIT Numerical Mathematics, vol.13, issue.2, pp.177-180, 1973.

J. Seiler and B. Tourniaire, A phenomenological analysis of melt progression in the lower head of a pressurized water reactor, Nuclear Engineering and Design, vol.268, pp.87-95, 2014.

R. L. Tellier, L. Saas, and S. Bajard, Transient stratification modelling of a corium pool in a LWR vessel lower head, Nuclear Engineering and Design, vol.525, pp.68-77, 2015.

B. Spindler, B. Tourniaire, and J. M. Seiler, Simulation of MCCI with the TOLBIAC-ICB code based on the phase segregation model, Nuclear Engineering and Design, vol.236, pp.2264-2270, 2006.

J. L. Rempe, D. L. Knudson, M. Cebull, and C. L. Atwood, Potential for in-530 vessel retention through ex-vessel flooding, Proc. of the OECD/CSNI Workshop on In-Vessel Core Debris Retention and Coolability, 1998.

, Apache Software Foundation, Apache commons math, 2016.

G. K. Gupta, R. Sacks-davis, and P. E. Tischer, A review of recent develop-535 ments in solving ODEs, Computing Surveys, vol.17, issue.1, pp.5-47, 1985.