Numerical solution of the complete Navier-Stokes equations for the simulation of unsteady flows

An extremely stable 'fully' implicit finite-difference method is described in detail. Although unconditional stability for the complete nonlinear equations has not been proved, it can be assumed that for stability the time-step restriction is less severe than for equivalent explicit or weakly implicit schemes. This aspect is particularly important for the simulation of strongly unsteady flows at high Reynolds numbers where it is desirable that the time step be adjusted with respect to the physical requirements of the unsteady flow variation rather than to satisfy a stability criterion. Some typical results obtained with this method are presented; they are results of calculations for a boundary layer flow and a plane Poiseuille flow disturbed periodically at the inflow boundary.