Finite Volume Method II: Pressure-Velocity Coupling in Incompressible Flows

The chapter gives a comparative overview of various coupling methods, highlighting their applicability, strengths, and computational considerations for incompressible finite-volume CFD simulations. This chapter introduces pressure–velocity coupling strategies used in the finite volume method for incompressible Navier–Stokes equations. It presents the foundational algorithms SIMPLE, SIMPLEC, PISO, and PIMPLE detailing their structure, and application to steady and unsteady flows. The formulation of the momentum predictor, pressure-correction equation, and velocity update is outlined for each scheme. Rhie–Chow interpolation and checkerboard suppression on collocated grids are also discussed. A benchmark lid-driven cavity problem is used to validate the SIMPLE algorithm.