Vorticity to velocity

[GerasimovIV]

Hello, thank you for you work. I have a misunderstanding with the obtaining velocity (for Navier Stokes equation) from given vorticity part. We actually need it for loss and you just wrote in the paper that it is easy, can you explain in more detail? If I understand correctly, that means we have to construct the inverse operator for curl, am I right? But it is not too easy 😅, or I something missed?

[zongyi-li]

For the 2d periodic Navier-Stokes equation, the velocity can be computed by first getting the stream function. The velocity is the derivative of the stream function (

physics_informed/train_utils/losses.py

Line 87 in 8246da4

f_h = w_h / lap

).

In general, for non-periodic case (like the cavity flow), it's non-trivial to get the velocity from vorticity. In this case we will the velocity-pressure formulation. (

physics_informed/cavity_flow.py

Line 249 in 8246da4

E1 = outt[..., 0] + out[..., 0]*outx[..., 0] + out[..., 1]*outy[..., 0] + outx[..., 2] - 1/Re*(outxx[..., 0] + outyy[..., 0])

)