Hello,

I'm trying to run a simulation on moving deforming structured grid. It uses the ALE scheme. deformation is done using arc based TFI. grid velocities are computed explicitly using Peric's space conservation law.

so what I need to know is in moving from t=n to n+1, after I've obtained u,v, must I interpolate them to the new grid? Or the u,v obtained are already for the new grid?

Thanks in advance.

Typically, the grid velocity is not expressed as a function of space and time. That would be unnecessarily complicated (makes no sense). Instead, you are dealing with the velocity of each grid point, i.e. the velocity is tied to the grid point, not to a fixed point in space. Does that answer your question?

Thank you Mani. But what I mean is regarding interpolation of the cell center velocities. The new answer I get after solving the NS equation - are they the velocities at the new cell center locations, so no interpolation is required... or are they the velocities at the old cell center locations, in that case interpolation is required. I've read of a few papers talking about "remapping".

You move your mesh and then solve correct? I've never used ALE so I am not sure of the exact procedure but I assume all of your discretization is based upon the new mesh so whatever variables you solve for are for the current mesh.

If you have accounted for the moving mesh effects in the discretisation, you don't need to do anything: the solution will be associated with the deformed mesh. In the Finite Volume method, the moving mesh effects shows up as a change fo cell volume between the iteration and as a mesh motion flux (volume swept by the face in motion) in convection terms.

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That's what I was trying to explain. Let's say your cell center ijk has the old position Xijk, and the old velocity Vijk. Now you perform your grid motion and use your interpolation scheme, and you get the new position Xnew,ijk and velocity Vnew,ijk. Those values (position and velocity) are directly applied to cell center ijk. There is no further interpolation necessary, because the position and velocity are tied to the node with index ijk, regardless where it is positioned.

Now, here is a different issue: If you are expressing your grid position in terms of cell centered nodes, then how are you calculating fluxes through the cell faces? Depending on your scheme you may still need to obtain the new position of the cell faces, and it that case you will indeed use interpolation.

YOu are probably using finite volume approach. Since your frame of reference is (locally) moving with your grid in the ALE approach, your newly computed data at n+1 is already for the new time-step and does not need to be interpolated at all.

In Perics approach you will see a total derivative in time and not the partial one, this also indicates that you have already transformed equations.