A strongly implicit simultaneous variable solution procedure for velocity and pressure in fluid flow problems

A strongly implicit solution procedure to be used on the algebraic equation system that results from the discrete modeling of the fluid flow equations governing mass and momentum transport in a two-dimensional domain is presented. In particular, the incompressible form of the equations where the coupling between the velocity and pressure fields poses cosiderable difficulty to conventional solution procedures is examined. This work is seen as the first attempt to use strongly implicit procedures in solving fluid flow problems formulated in terms of the primitive u, v, and p variables. A derived equation for pressure retaining significant coupling to the velocity field is used, and a strongly implicit procedure for the resulting coupled system of equations is derived. The pressure equation here takes the place of the continuity equation. The procedure is demonstrated by applying it to the driven cavity problem for Reynolds numbers of 100, 400, and 1000. The procedure is shown to perform well, giving rapidly convergent, economical solutions.