Problem with very high gradients
i'm trying to implent a new boundary condition for which i need the second derivative of U in normal direction. (slip velocity)
In order to get a second order derivative (which isn't laplacian) i'll do:
| Ux,xx Uy,xx Uz,xx |
d2U=| Ux,yy Uy,yy Uz,yy |
| Ux,xx Uy,xx Uz,zz |
This works great but only to a certain dimension of the mesh. Attached to this post there are 2 cases and a modified rhoPimpleFoam solver.
the first case "microKanal2"(Kanal:channel in german) has a height of 1.68e-3 meters. The velocity field result in a parabola with an increasing maximum for higher x values. Therefore the first derivative dU shows in y direction a linear function. The tensor compoent(3) Ux,yy should be a a constant value for a cross section of the channel, but changing with the position of x (see picture).
the second case "microKanal" has a height of 1.68e-4 meters. For component 3 of the tensor there are following values (see attached picture)
The field isn't smooth at all it suddenly jumps to another value. A possible reason for that could be that double isn't accurate enough.
Does anyone know what the problem is and how it can be solved?
Where did you write these codes?
the code is in the rhoPimpleFoam.C after the pimple loop
or what do you mean exactly?
I am facing the same problem.
I need to calculate second derivative e.g for field F i need F_xx, F_yy.
I did it the same way as you.
gradF = fvc::grad(F) // vector of first derivatives
gradgradF = fvc::grad(gradF) // tensor of second derivatives
as far as gradF is fine/smooth, gradgradF is not anymore ...
Were you able to solve this problem ?
for what do you need it?
please see my post located at:
where I am writing about other way of dealing with second order mixed derivative.
What do you think about that ?
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