The application of preconditioning in viscous flows

Abstract

A time-derivative preconditioning algorithm that is effective over a wide range of flow conditions from inviscid to very diffusive flows and from low speed to supersonic flows has been developed. The algorithm uses a preconditioning matrix that introduces well-conditioned eigenvalues while simultaneously avoiding nonphysical time reversals for viscous flows. The resulting algorithm also provides a mechanism for controlling the inviscid and viscous time step parameters at very diffusive flows, thereby ensuring rapid convergence for very viscous flows as well as for inviscid flows. Computational capabilities are demonstrated through computation of a wide variety of problems. Convergence rates are shown to be accelerated by as much as two orders of magnitudes, while providing solutions that are indentical to those obtained without preconditioning method. © 1993 Academic Press, Inc.