Solving Poisson Equation for pressure with all-Neumann boundary conditions

[mec...@menudo.uh.edu]

Hi! Let me begin by thanking those who replied to my earlier message
on influence of outflow b.c.

Now I am trying to solve a Poisson equation (for pressure in
incompressible flows) with all Neumann boundary conditions. The way
I implement the boundary condition is to first write a finite-difference
representation of dp/dn on the boundary (in my case it is a five-point
fourth-order scheme), and then use the formula to modify the finite
difference representation of the Poisson equation in the field.

The problem is, after I obtained the pressure values, I use the same
FD scheme to calculate dp/dn on the boundaries and they are NOT the
same as the original B.C., and the differences are NOT diminishing
when I reduce the mesh size.

I would appreciate any help on this. - I did check the solver using
some exact solutions, and they work fine. It is only when I try to
calculate the pressure for the Navier-Stokes equation that the problem
comes up.

Thanks a lot!

Jianfeng Zhang
Dept of Mech. Engr.
University of Houston

[Jay D. Morris]

>Now I am trying to solve a Poisson equation (for pressure in
>incompressible flows) with all Neumann boundary conditions. The way

>Jianfeng Zhang

>Dept of Mech. Engr.
>University of Houston

The Poisson equation is an Elliptic PDE. Are all the boundarys closed?
If not, the boundary conditions would be insufficient for well-posedness.

Jay Morris
Dept of Mech. Eng.
Yale University