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
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!
In my case, U is the unknown velocity in N-S equation, x is the coordinate. they are independent to each other. What I am looking for is an analytical expression for my coding. I am sure it's solvable in some way as I am not the first to encounter this problem.