A Unified Formulation of the Segregated Class of Algorithms for Fluid Flow at All Speeds

In this article, the segregated SIMPLE algorithm and its variants are reformulated, using a collocated variable approach, to predict fluid flow at all speeds. In the formulation, a unified, compact, and easy-to-understand notation is employed. The SIMPLE, SIMPLER, SIMPLEST, SIMPLEM, SIMPLEC, SIMPLEX, PRIME, and PISO algorithms that are scattered in the literature and appear to a non versed computational fluid dynamics (CFD) user as being unrelated, are shown to share the same essence in their derivations and to be equally applicable for the simulation of incompressible and compressible flows. Moreover, the philosophies behind these algorithms in addition to their similarities and differences are explained.