A two-stage pressure correction technique for the incompressible Navier-Stokes equations

Abstract

This paper describes a new strongly-implicit line solution technique for the steady incompressible NavierStokes equations. The formulation leads to a second order accurate block tri-diagonal system of linear equations in term of primitive variables. It includes a new two stage pressure correction scheme which leads to extremely rapid convergence of all variables. The resulting computational model is structured so as to allow both the partiallyparabolized and the full NavierStokes equations to be solved with only trivial changes to the computer code, It has been tested for both internal and external flow problem and has proven to be both accurate and fast when applied to the solution of both the parabolized and the full form of the Navier -Stokes equations with dramatic reductions in computer time for both form of the equations. BACKGROUND

Prediction of steady and unsteady flow and heat transfer over a cylinder in crossflow using a space-time marching algorithm

“…A successful attempt to increase convergence rates in steady cases was made by Bentson and Vradis (1987). They solved both the partially parabolized and the full Navier-Stokes equations in incompressible form using a space marching scheme on a staggered grid.…”