A TIME-SPLITTING APPROACH TO SOLVING THE NAVIER-STOKES EQUATIONS

This note describes a time-splitting approach for integrating the comp ressible Navier-Stokes equations. Attention is focussed on the constru ction of a fast implicit solver for the numerical integration of the s plit diffusion sub-problem in the Navier-Stokes equations. The propose d diffusion solver is used in conjunction with a high resolution Euler solver by means of convection diffusion time-operator splitting and i s therefore particularly simple to incorporate into existing Euler cod es. Convection-diffusion splitting allows appropriate methods to be ap plied separately to the convective and diffusive parts of the Navier-S tokes equations and can significantly reduce the cost of simulating vi scous flows, since the convective solver is no longer bound by viscous time-step restrictions. We describe an uncoupled approach for the sol ution of the diffusion equations, where a direct, low storage implicit solution is possible with only scalar tridiagonal matrix inversionsc. (Copyright (C) 1996 Elsevier Science Ltd)