CFD Online Logo CFD Online URL
Home > Forums > General Forums > Main CFD Forum

Poisson Solver question

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Search this Thread Display Modes
Old   August 11, 2005, 15:30
Default Poisson Solver question
Posts: n/a
Hi All:

This is really a question in harmonic analysis - Let me state the question and then the CFD setting.

I am solving the Poisson equation in 2D

Lap(u) = f(x,y)

in a 2d doamin. There are both Dirchlet and Neumann conditions on the boundary. My question Is:

1) To what extent does the solution u(x,y) depend on values of f(x,y) ON the boundary ?

My guess is that on segments where there is a Dirichlet condition, values of f on the boundary do not affect the solution at all. But what about on other boundary segments ?

The setting of this is when you are solving for the stream function from the vorticity. Typically you know f(x,y) only on interior points and do not know it on the boundary.

Thanks !

  Reply With Quote

Old   August 11, 2005, 20:24
Default Re: Poisson Solver question
Posts: n/a
If the Poisson equation is valid throughout the domain (including the boundary), the Laplacian of u is given by f everywhere, including the boundary. That means, even though u itself (Dirichlet) or its gradient (Neumann) are specified on the boundary, the Laplacian there still depends on f, and that should have some effect on the interior solution.
  Reply With Quote

Old   August 11, 2005, 23:56
Default Re: Poisson Solver question
Posts: n/a
This is an interesting issue. What I want to emphasize is that the equation is not valid at the boundary but valid in the neighborhood of the boundary, no matter of the BC being adopted.
  Reply With Quote

Old   August 12, 2005, 04:37
Default Re: Poisson Solver question
Posts: n/a
The equation must be valid at the boundary if the solution of the boundary value problem is to be solved. It's just a matter of how you interpret the limiting process as the boundary is approached; i.e. the derivatives are one sided at the boundary.

Possibly more important for your question is the compatability relation which tells you whether the problem is solvable; e.g. integrate your equation over the whole domain and apply the divergence theorem.
  Reply With Quote


Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
FFT solver for Poisson equation mranji1 Main CFD Forum 1 November 16, 2009 01:12
question about solver output... vijeshjoshi23 CFX 1 August 10, 2009 06:23
interface tension question with interFoam solver openTom OpenFOAM Running, Solving & CFD 4 May 29, 2009 13:18
Beginner question OddEven Decoupling in SIMPLE Solver brooksmoses OpenFOAM Running, Solving & CFD 2 November 9, 2005 19:38
Poisson solver Steve Main CFD Forum 6 July 22, 2004 21:16

All times are GMT -4. The time now is 14:07.