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Comparison of finite element techniques for solidification problems
Author(s) -
Dalhuijsen A. J.,
Segal A.
Publication year - 1986
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.1620231003
Subject(s) - finite element method , backward euler method , mathematics , iterative method , grid , algorithm , matrix (chemical analysis) , computer science , mathematical optimization , materials science , thermodynamics , mathematical analysis , euler equations , physics , geometry , composite material
The accuracies of the computed temperatures of a liquid in a corner region under freezing conditions are compared for various fixed‐grid finite element techniques using the analytical solution for this problem as a reference. In the finite element formulation of the problem different time‐stepping schemes are compared: the implicit Euler‐backward algorithm combined with an iterative scheme and two three‐time‐level methods—the Lees algorithm and a Dupont algorithm, which are both applied as non‐iterative schemes. Furthermore, different methods for handling the evolution of latent heat are examined: an approximation method suggested by Lemmon and one suggested by Del Giudice, both using the enthalpy formulation as well as a fictitious heat‐flow method presented by Rolph and Bathe. Results of calculations performed with the consistent heat‐capacity matrix are compared with those performed with a lumped heat‐capacity matrix.