Abstract: An implicit muIti-grid technique for computing three-dimensional algorithm proposed by Ni and Johnson,where the Reynolds-averaged Navier-Stokes equations are solved, consecutively,from the-gine;levels through the coarse ones,using MacConT1ack’s two-step explicit scheme,in conjunction with the spaee-varying time-marching proeedure. An iteration scheme is constructed using the residue between the solution in two time step to approx-imate the time derivative of the fluxes,so that the additional computations on the Jocobian matrices presisted in Ni's original scheme can be eliminated.The scheme wilI thus reduee the CPU time substantially,and accelerate significantly the convergence.The technique developed isemployed to simulate the internal flows of nonaxisymmetric,two一dimensional,convergingd*verging nozzles.Numerical results are found in good agreement with the available experimental data,revealing high reliability of the developed technique in complex flow simulation。

Key words: multiple-grid algorithm, explicit scheme, N-S equations, 2-D nozzles