Comparison of finite element techniques for solidification problems

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Abstract
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.

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