For unsteady two-phase flows, the widely-used numerical approaches for solving continuity and momentum equations are fractional-step method and SIMPLE-family algorithms. The advantage of the fractional-step method is that the convergence rate is fast and the disadvantage is that the initial value problem is conditional stability. The SIMPLE-family algorithms are absolute stability for the initial value problem; however, their convergence rates are slow. For overcoming the disadvantage of the traditional SIMPLE-family algorithms, IDEAL algorithm was introduced. The convergence rates of SIMPLE-family and IDEAL were compared by two unsteady two-phase flow problems. It was found that IDEAL could enhance the convergence rate greatly, about 6-87 times over SIMPLE-family. Therefore, it could be concluded that IDEAL overcame the disadvantages and combined the advantages of the fractional-step method and the SIMPLE-family algorithms.
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