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An object oriented implementation of a front tracking finite element method for directional solidification processes
Author(s) -
Sampath Rajiv,
Zabaras Nicholas
Publication year - 1999
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/(sici)1097-0207(19990330)44:9<1227::aid-nme471>3.0.co;2-r
Subject(s) - finite element method , galerkin method , mechanics , transient (computer programming) , petrov–galerkin method , conservation of mass , tracking (education) , computer science , mechanical engineering , mathematics , physics , engineering , thermodynamics , operating system , psychology , pedagogy
This paper focuses on the numerical simulation of phase‐change processes using a moving finite element technique. In particular, directional solidification and melting processes for pure materials and binary alloys are studied. The melt is modelled as a Boussinesq fluid and the transient Navier–Stokes equations are solved simultaneously with the transient heat and mass transport equations as well as the Stefan condition. The various streamline‐upwind/Petrov–Galerkin‐based FEM simulators developed for the heat, flow and mass transport subproblems are reviewed. The use of classes, virtual functions and smart pointers to represent and link the particular simulators in order to model a phase change process is discussed. The freezing front is modelled using a spline interpolation, while the mesh motion is defined from the freezing front motion using a transfinite mapping technique. Various two‐ and three‐dimensional numerical tests are analysed and discussed to demonstrate the efficiency of the proposed techniques. Copyright © 1999 John Wiley & Sons, Ltd.