A Stable Alternating Direction Method For Simulating Multidimensional Solidification Problems

Application of the Alternating Direction Implicit (ADI) method to study solidification problems reveals some drawbacks. At the interface between different‐materials, temperature oscillations may be recorded at the simulation start which eventually may cause instability. The problems originate from the explicit temperature calculation. Shortcomings may be eliminated by substituting the explicit temperature calculation by an implicit one which is carried out on a limited number of adjacent elements. Results of real solidification problems show that the modified method behaves better than the original ADI method. The new procedure, which is formulated in terms of the finite volume method, eliminates the occurrence of physically incorrect temperature calculations and oscillations initially present in the vicinity of the interface between different materials. When applied to the three‐dimensional solidification problem of the sand coated die, simulation results are in good agreement with experimental data.