Dear friends: When I used LU-SSOR method for the Euler solution of steady case,I found that the pressure distribution was far from the final results with the explicit method while the average derivative value of density to time was very small.I also found that the time to converge the pressure distribution was nearly the same as that of explicit method. I want to know the reason for the above and how to get high efficiency. The time stepping scheme in explicit method is five step Runge-Kutta method, and the space discretization in both methods is Jameson's Finite Volume Method.Thinks a lot for your reading! Waiting for your reply ...

Aiming, it may be that you have to optimise the artificial damping for the implicit scheme you are using. Antony Jameson published a paper on th LU scheme that you may want to peruse. also remember that the five step runge kutta scheme probably has a higher allowable CFL than the more commonly used 4 step scheme (for which the higher allowable CFL is ~2.8). also the explicit scheme can also take advantage of acceleration techniques like residual averaging and enthalpy damping. i don't know if you wrote the code yourself, if not these features may be used without your knowing. anyhow the runge kutta scheme can be modified to give fast convergence (and it's optimal settings are well known). so it may be that you have a well tuned runge kutta code and a not so well tuned LU code