Despite the large increase in computer power and the advances in solver technology, unsteady flow problems still may require a vast amount of computing time. In this work two approaches are investigated that should lead to a reduction in computing times for unsteady subsonic flows. In the first part of this work a new refinement strategy for grid adaptation is proposed that enables the user to a priori define the maximum usable computer resources. In the second part of this work a Jacobian-free Newton-Krylov algorithm is tailored for unsteady subsonic flow problems. With this algorithm...