This book introduces a new generation of superfast algorithmsfor the treatment of the notoriously difficult velocity-pressure couplingproblem in incompressible fluid flow solutions. It provides all the necessary details for the understanding andimplementation of the procedures. The derivation and construction of thefully-implicit, block-coupled, incomplete decomposition mechanism are given ina systematic, but easy fashion. Worked-out solutions are included, withcomparisons and discussions. A complete program code is included for fasterimplementation of the algorithm. A brief literature review of the developmentof the classical solution procedures is included as well.