In this paper,the multigrid method is presented associated with LUSGS implicit scheme to calculating the low speed flow field around the NLR7301 case#1 and the transonic flow field around the DLRF4 wing-body configuration,all results conf.

An efficient numerical method that contains the new LU type implicit scheme and the modified fourth order high resolution MUSCL TVD scheme is proposed for solving the compressible Navier Stokes equations.

A new implicit scheme based on the LU-SGS scheme in conjunction with diagonalization and Cramer s rule (LUSGS-DC) has been developed for solving the compressibleNavier-Stokes equations.

We deduce the strongly implicit procedure method for the seven-diagonal matrix which is obtained from the finite differentiate method of the elliptic equation in 3 dimensions,give the iterative formation,prove the convergence of the algorithm and analyze the choice of the iterative parameter.

Based on one example, the influences of the time step or grid step on the accuracy of the calculation results of the air flow distrbution numerical simulation in the implicit scheme was discussed and analyzed to acquire the agreeable calculation results,the author's idea has been presented with the analysis.