# Mesh restrictions for high Re compressible ramp

Hello, I simulate compressible ramp case at Re=6.08e7 and Ma = 2.87. The height of the first grid is 2.06e-4, and the aspect-ratio is very big. NaNs always comes up in the calculation. And I set aspect-ratio at about 200, it also comes up NaNs. Does the aspect ratio have to be around 20? If so, the grid will be finer.

That’s quite a high Reynolds number. If you’re trying to perform LES of this case, we would typically say that the first grid point should be at y^+=1. For this case y^+=1 is at y\approx5\times10^{-7}, so for p=3 this would probably mean your first cell needed to be about 3\times10^{-6}.

This will probably be contributing to your instability, as without sufficient wall resolution, your no-slip wall are effectively a discontinuity. As a first pass, can you try reducing your Reynolds number to 6.08e4?

Also your aspect ratio does seem a bit high, have a look at Paul Tucker’s book, he has some good rules of thumb for wall resolved LES in terms of x+, y+, z+.

As you said, y is 5e−7, so for p=3, I think the first cell is 5e-7*(p+1) = 2e-6, Why 3e-6?

To compare with the experimental data, I use the dimentional value. And reducing my Reynolds number to 6.08e6, then the first cell is 3e-5. The aspect ratio is over 2000, and now the grid is too fine. Are there other ways to reduce the aspect ratio? I don’t know if there is a problem with the setup of the initial file.

The ini file and pw grid are attached.

Best regards

The points inside the element are not equispaced, and I recall that for a p=3 quad with Gauss–Legendre points, the first point is about 15% of the way into the element. But this might be slightly off.

Sadly, the only way to reduce the aspect ratio here is to decrease the mesh spacing in the streamwise direction. You probably want to aim for an aspect ratio of x:y no larger than around 10-20. This is based on the scale of features in a turbulent boundary layer.