PDE 2D

[holti]

Hello,

I would like to calculate the two dimensional flow field w(x,y) inside  x,y element of [0;L(x,y)] described by the attached PDE:

Does anyone have an idea how to solve this Problem?

Thanks in advance.

[-MFra- · Accepted solution]

Hi holti,

Try to use the Mathcad15 operator PDEsolve() which, by the way, is quite complicated . Otherwise, you should create e rutine  which uses the approximation of the given p. d. equation, by the finite differences method (after having studied the stability and the convergence of the method.).

[holti]

Hi MFranc,

thank you for your answer. I am using ptc mathcad prime 5.0.0.0. There is no PDEsolve Option, as I see in the function list.

Implicit FDM is an Option but a lot of work and sometimes unstable, unfortunately. I was hoping to find a good solver for that.

[-MFra-]

To examine solutions or attempts to solve partial differential equations, by community members, with pdesolve (), do a search as shown in the following figure:

(Remark:you should better define the upper extremes of the double integral )

[holti]

Hello MFranc

I have finally accepted that I have to approach it by 2D FDM.

This is the preliminary result for 2 Dirichlet BC's and 2 Neumann BC's with a constant force:

Thank you!

[terryhendicott]

Hi,

https://peer.asee.org/teaching-fluid-mechanics-using-mathcad.pdf

The above link may prove helpful.

Cheers

Terry