Comparison of the SMAC, PISO and iterative time-advancing schemes for unsteady flows

Abstract

Calculations of unsteady flows using a simplified marker-and-cell (SMAC), a pressure-implicit splitting of operators (PISO) and an iterative time-advancing (ITA) scheme are presented. A partial differential equation for incremental pressure is used in each time-advancing scheme. Example flows considered are a polar cavity flow starting from rest and self-sustained oscillatory flows over a circular and a square cylinder. For a large time-step size, the SMAC and ITA schemes are more strongly convergent and yield more accurate results than the PISO scheme. The SMAC scheme is the most efficient computationally. For a small time-step size, the three time-advancing schemes yield equally accurate Strouhal numbers. The capability of each time-advancing scheme to accurately resolve unsteady flows is attributed to the use of a new pressure correction algorithm that can strongly enforce the conservation of mass. The numerical results show that the low frequency of the vortex shedding is caused by the growth time of each vortex shed into the wake region.