We investigate the effectiveness of two extrapolation-based methods aiming to approximate the initial state required by an iterative solver in simulations of unsteady flow problems. The methods lead to about a ten-fold reduction in the iteration count while requiring only negligible computational overhead. They are particularly suitable for parallel computing since they are based almost exclusively on data stored locally on each processor. Performance has been evaluated in simulations of turbulent flow in a stenosed carotid artery and also in laminar flow in a very large domain containing the human intracranial arterial tree.
