| 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. |
