Stefan Problem through Extended Finite Elements: Review and Further Investigations
Open Access
- 21 September 2009
- journal article
- research article
- Published by MDPI AG in Algorithms
- Vol. 2 (3), 1177-1220
- https://doi.org/10.3390/a2031177
Abstract
A general review of the extended finite element method and its application to the simulation of first-order phase transitions is provided. Detailed numerical investigations are then performed by focusing on the one-dimensional case and studying: (i) spatial and temporal discretisations, (ii) different numerical techniques for the interface-condition enforcement, and (iii) different treatments for the blending elements. An embeddeddiscontinuity finite element approach is also developed and compared with the extended finite element method, so that a clearer insight of the latter can be given. Numerical examples for melting/solidification in planar, cylindrical, and spherical symmetry are presented and the results are compared with analytical solutions.Keywords
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