# How to compute this weird derivative?

• May 10th 2010, 04:22 PM
bearcat
How to compute this simple but weird derivative?
Hello,

I am working on numerical solution of incompressible fluid dynamics problem. I need to compute the Jacobian of a viscous flux. I have to deduct some derivatives like this

$\frac{\partial (\frac{\partial U}{\partial X})}{\partial U}=?$

U, X are independent to each other.

Some people say the result is absolutely not zero, but I still could not find an analytical answer. I wonder this will turn out into a derivative operator rather than an expression of fixed value. If an analytical expression is not possible, how to handle this in a finite difference method?

Thank you and have a good day!

Bearcat
• May 10th 2010, 04:54 PM
Anonymous1
Quote:

Originally Posted by bearcat
Hello,

I am working on numerical solution of incompressible fluid dynamics problem. I need to compute the Jacobian of a viscous flux. I have to deduct some derivatives like this

$\frac{\partial (\frac{\partial U}{\partial x})}{\partial U}=?$

Some people say the result is absolutely not zero, but I still could not find an analytical answer. I wonder this will turn out into a derivative operator rather than an expression of fixed value. If an analytical expression is not possible, how to handle this in a finite difference method?

Thank you and have a good day!

Bearcat

I've seen something like this before...

What you want to do is:

(1)Take the partial of U w.r.t. x. Denote the result by L.

(2)Transform L so that it is in terms of U. (This is the hard part)

(3)Take the partial of Transform(L) w.r.t. U.

Can you post what U is?
• May 10th 2010, 06:06 PM
bearcat
I suspect it's possibly $\frac{1}{\delta _{x}}$.