The application of preconditioning in viscous flows

The present time-derivative preconditioning algorithm is effective in flow conditions ranging from inviscid to very diffusive flows, as well as low subsonic to supersonic flow velocities. By means of a preconditioning matrix that (1) introduces well-conditioned eigenvalues and (2) avoids nonphysical time reversals for viscous flows, a mechanism is obtained which controls the inviscid and viscous time-step parameters at very diffusive flows. These capabilities are demonstrated for a variety of sample problems; convergence rates of solutions that are indistinguishable from those obtained without preconditioning are shown to be accelerated by as much as two orders of magnitude.