[zhanglei]

hi everyone, I'm working on a program solving the external inviscid flow around an airfoil. I am using unstructured mesh,Jameson cell-centered scheme,non-reflect far field boundary condition as well as local time step & explict residual smoothing. I'm using these schemes to solve the flow around naca0012 airfoil under an external flow speed ranging from subsonic to supersonic and they work well. later for optimizing purpose I tried to use multigrid method with these schemes.Right after that the program diverge quickly and I find that whenever I turn off the explicit residual smoothing option the whole progam converge again. without this option I can only use a CFL number up to around 1 to guarantee the convergence of the program( with a CFL of 1 the program will converge after 1500 iterations when the fixed acuracy is reached,without multigrid and with the same CFL number the program will converge after 15000 or even more iterations). It just seems that the explicit residual smoothing method doesn't work with multigrid, which is likely to be wrong since I have read some papers concerning these methods using together. when used in runge-kutta steps, the residual should add forcing function and become a "modified residual". Which of the residual and the "modified residual" is the one I ought to smooth? If anybody has solved the problem I met, what's the biggest CFL number you could use?