[Joachim]

Hey everyone!

I have a question regarding moving grid algorithms. Let's say I have a working NS code, and I want to implement the ALE formulation to run oscillating airfoils. Please correct me if I am wrong:

1. I modify the convective fluxes only, including the term -Vg*Q everywhere (Q is the state vector and Vg the normal grid velocity at the face). The normal convective flux at the face becomes Fc(moving) = Fc(static) - VgQ

2. I do not modify the boundary conditions. For example, at a solid wall, I have v = 0 and not v= vg.

3. The grid is non-deforming, and is only translating/rotating with a prescribed motion. Therefore the grid velocity is determined analytically. I recompute the location of the grid points, grid metrics, etc at each physical time step.

Is that correct? I am having an issue when computing the fluxes at the walls. Using the continuity equation as an example, the normal convective flux for a moving grid is

Fcm = rho*(Vn - Vg) (Vn is the contravariant velocity, not relative)

At the wall, I have Vn = 0 in an inviscid case, so that Fcm = -rho*Vg --> This does not work...

If I put Vn = Vg, so that Fcm = 0, then it gives the correct results...

Is there something I have misunderstood?
Thank you very much for your help!

Joachim