Improvements in speed for explicit, transient compressible flow solvers

Several explicit high-resolution schemes for transient compressible flows with moving shocks are combined in such a way so as to achieve the highest possible speed without compromising accuracy. The main algorithmic changes considered comprise the following: replacing limiting and approximate Riemann solvers by simpler schemes during the initial stages of Runge-Kutta solvers, and only using limiting and approximate Riemann solvers for the last stage; automatically switching to simpler schemes for smooth flow regions; automatic deactivation of quiescent regions; and unstructured grids with cartesian cores or embedded cartesian grids. The results from several examples demonstrate that speedup factors of 1:4 are attainable without compromising the accuracy of the traditional FCT schemes. Copyright (c) 2007 John Wiley & Sons, Ltd.