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Abstract: A series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper. These methods are often referred to in the literature as projection methods, and can be classified into three classes, namely the pressure-correction methods, the velocity-correction methods, and the consistent splitting methods. For each class of schemes, theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed. The essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners. [Copyright &y& Elsevier]