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A temperature‐based formulation for finite element analysis of generalized phase‐change problems
Author(s) -
Celentano Dsego,
Oñate Eugenio,
Oller Sergio
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620372004
Subject(s) - finite element method , jacobian matrix and determinant , convergence (economics) , mathematics , stability (learning theory) , mixed finite element method , extended finite element method , phase change , numerical analysis , matrix (chemical analysis) , phase (matter) , state variable , mathematical optimization , mathematical analysis , computer science , structural engineering , engineering , physics , materials science , engineering physics , quantum mechanics , machine learning , economics , composite material , economic growth , thermodynamics
A finite element formulation for solving multidimensional phase‐change problems is presented. The formulation considers the temperature as the unique state variable, it is conservative in the weak form sense and it preserves the moving interface condition. In this work, an approximate jacobian matrix that preserves numerical convergence and stability is also derived. Furthermore, a comparative analysis with other different phase‐change finite element techniques is performed. Finally, several numerical examples are analysed in order to show the performance of the proposed methodology.