I am trying to use multigrid in 3D complex flowfield calculation by using Euler eqs. and I have get it , the only thing is that when enthalpy damping is on , multigrid does not work , otherwise it convergence well .

-1) As a first check you could try just to use the relaxation scheme on the fine grid to see if the problem is related to the relaxation scheme itself or to the multigrid. This of course might take much more CPU than the multigrid, but at least you should be able to check whether the schme converges or divereges.

-2) When advancing a full time step one usually takes only a 'portion' of the correction:

U becomes U+a*dU

where dU is the correction and a is a constant smaller than one. You can also try to decrease a to a smaller value to check the convergence of the multigrid in general.

-3) your equations are incompressible and inviscid. What is the enthalpy damping term in your case?

PG.

It seems to me that he is using compressible equations, more likely using finite volume based time marching scheme. I haven't heard anyone using incompressible INVISCID equations. It simply reduce to the full potential equation if no vorticity is introduced in the boundaries.

I am using cell-centered finite volume +Runge-Kutta for inviscid Euler eqs for external flow , which is same as Hongjun Li 's method . The fact is that when enthalpy damping is off , the residual decreases 10-order and once enthalpy damping is on , the residual drcrease 4-order and then frozen as a constant .

(1). I am not going to solve your multigrid problem. (2). So, you can go back to the single grid method and check out the difference in convergence rate with /or without the damping term. (3). If you were able to get fast convergence without damping term using multigrid method for Euler equation, then apparently there's no need to include the damping term in it, right? ( anyway, when a damping term is added to an inviscid equation, I don't think it can stay inviscid. Unless you can show that the term added has no effect on the final results. That is also unlikely.)

Enthalpy damping is different from other damping terms. The enthalpy damping is a 'forceing term' to speed up convergence to steady state solutions. It is an addational term which is proportional to the difference of the local enthalpy (in the not converged solution) and the final steady state enthalpy (which is constant everwhere in inviscid flow). When the solution reaches steady state, this term become zero so that it will not affect the final solutions.

I also don't know why the problems happen to Mr. Yao. But I will suggest that you may just turn off the E-damping terms because when you extend you code to viscous or unsteady flows, you have to turn-off this terms anyway.

HL

(1). I think he is solving transient Euler equation using Runge-Kutta method.