A STRONGLY COUPLED TIME-MARCHING METHOD FOR SOLVING THE NAVIER-STOKES AND K-OMEGA TURBULENCE MODEL EQUATIONS WITH MULTIGRID

摘要

Many researchers use a time-lagged or loosely coupled approach in solving the Navier-Stokes equations and two-equation turbulence model equations in a time-marching method. The Navier-Stokes equations and the turbulence model equations are solved separately and often with different methods. In this paper a strongly coupled method is presented for such calculations. The Navier-Stokes equations and two-equation turbulence model equations, in particular, the k-omega equations, are considered as one single set of strongly coupled equations and solved with the same explicit time-marching algorithm without time-lagging. A multigrid method, together with other acceleration techniques such as local time steps and implicit residual smoothing, is applied to both the Navier-Stokes and the turbulence model equations. Time step limits due to the source terms in the k-omega equations are relieved by treating the appropriate source terms implicitly. The equations are also strongly coupled in space through the use of staggered control volumes. The method is applied to the calculation of flows through cascades as well as over isolated airfoils. Convergence rate is greatly improved by the use of the multigrid method with the strongly coupled time-marching scheme. (C) 1996 Academic Press, Inc. [References: 27]