How to compute UDS fourth order gradient
 

Hi! Guys!
I computate fourth order derivative with UDS through Gauss's divergence theorem.

We can obtain second order derivative of Φ through integrating Laplacian of Φ at cell c0.
For computing fourth order derivative, the idea is that using Gauss's divergence theorem again and let the second order derivative to be the UDS.

i was confusing that seconder order gradient is a vector here, and not like the original Φ, which is a scalar.

how to solve this problem?

I directly use C_face_loop to present second order derivative first.
c_face_loop(c,t,n)
{
F_AREA(A,C_FACE(c,t,n), C_FACE_THREAD(c,t,n));
At = NV_MAG(A);
Aterm = At/C_VOLUME(c,t);
NV_DS(Grad2, +=, C_UDSI_G(c,t,GRAD_1)[0], C_UDSI_G(c,t,GRAD_1)[1], C_UDSI_G(c,t,GRAD_1)[2],*,Aterm);
}
For computing fourth order derivative, I use magnitude of second order gradient to define a UDS.
C_UDSI(c,t,GRAD_1) =NV_MAG(Grad2)

The fourth gradient is then be,
c_face_loop(c,t,n)
{
F_AREA(A,C_FACE(c,t,n), C_FACE_THREAD(c,t,n));
At = NV_MAG(A);
Aterm = At/C_VOLUME(c,t);
NV_DS(Grad4, +=, C_UDSI_G(c,t,GRAD_1)[0], C_UDSI_G(c,t,GRAD_1)[1], C_UDSI_G(c,t,GRAD_1)[2],*,Aterm);
}

I was wondering if this is correct to slove it.

Could you please give me some advise?

Expecting your early reply!!

Many thanks,

Gradients
 

Hi Emma,

I read your post but I cannot help you, sorry. But maybe you can help me with a problem that I had for months.

I program a UDF and I need the second order gradient of temperature or any UDSI. I see that you caluculate it by: "integrating Laplacian of Φ at cell c0" The code is:

"c_face_loop(c,t,n)
{
F_AREA(A,C_FACE(c,t,n), C_FACE_THREAD(c,t,n));
At = NV_MAG(A);
Aterm = At/C_VOLUME(c,t);
NV_DS(Grad2, +=, C_UDSI_G(c,t,GRAD_1)[0], C_UDSI_G(c,t,GRAD_1)[1], C_UDSI_G(c,t,GRAD_1)[2],*,Aterm);
}
"

The problem is that I dont fully understand the operation. Is there any reference to this operation?

I would be very happy if you could help me, this problem starts to be hopeless!
Thank you!
/Andreas