The accuracy, stability, and cost of the standard finite-element method, (Standard), Matrix method method of Ohnaka, and alternating-direction, implicit finite-difference method (ADI) have been compared using analytical solutions for two problems approximating different stages in steel ingot processing. The Standard and Matrix methods both employ triangular elements and were compared using the Dupont, Lees, and Crank-Nicolson time-stepping techniques. Other variables include mesh and time-step refinement, type of boundary condition formulation, and the technique for simulating phase change. The best overall combination of methods investigated for modeling two-dimensional, transient, heat conduction problems involving irregular geometry was the Dupont-Matrix method with a lumped boundary condition formulation and temperature dependent properties evaluated at time level two, coupled with the Lemmon latent-heat evolution technique if phase change is involved. For problems with simple geometry, the ADI method was found to be more cost effective.
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