Abstract: Two types of preconditionings coupled with the GMRES algorithm for the two-dimensional Euler equations are presented.An approach is used for reducing the memory requirement of GMRES algorithm and preserving its efficiency.With the calculations of two inviscous flows,the GMRES algorithm and the associated two preconditionings are analyzed,and its comparison with the DDADI method is also presented.The calculation results of the NACA0012 airfoil transonic flow and the supersonic GAMM flow show that the GMRES algorithm coupled with the two preconditionings has superior advantage on convergence rate compared to DDADI method.Furthermore,from the results it can be seen that the LUSGS preconditioning is slightly better than the ILU preconditioning.

Key words: Euler equations, GMRES algorithm, preconditioning