A Helmholtz pressure equation method for the calculation of unsteady incompressibl eviscous flows

A time‐implicit numerical method for solving unsteady incompressible viscous flow problems is introduced. The method is based on introducing intermediate compressibility into a projection scheme to obtain a Helmholtz equation for a pressure‐type variable. The intermediate compressibility increases the diagonal dominance of the discretized pressure equation so that the Helmholtz pressure equation is relatively easy to solve numerically. The Helmholtz pressure equation provides an iterative method for satisfying the continuity equation for time‐implicit Navier–Stokes algorithms. An iterative scheme is used to simultaneously satisfy, within a given tolerance, the velocity divergence‐free condition and momentum equations at each time step. Collocated primitive variables on a non‐staggered finite difference mesh are used. The method is applied to an unsteady Taylor problem and unsteady laminar flow past a circular cylinder.