CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

Poisson equation fourier transform before discretization

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

Reply
 
LinkBack Thread Tools Display Modes
Old   November 9, 2010, 13:00
Default Poisson equation fourier transform before discretization
  #1
New Member
 
Yohei Kawazura
Join Date: Oct 2010
Posts: 3
Rep Power: 6
yohey44 is on a distinguished road
Hi,

I tried to solove Poisson equation by spectral method.
Referring this note(http://www.physics.buffalo.edu/phy41...6/ch6-lec2.pdf), I pluged FFT for discretized form as,
(U_j+1,k + U_j-1,k + U_j,k+1, Uj, K-1 - 4U_j,k)/h^2 = -f_j,k.

Fourier transform is defined as,
U'_m,n=1/N*Sum_{j=0}^{N-1}(W^-{mj+nk}U_j,k),
W = exp(2*i*pi/N)

Then I obtain,
U'_m,n = -h^2*f_j,k/(W^m+W^-m+W^n+W^-n-4).

With inverse transfom, seemingly correct result is obtained.

However, I think fourier transform before discretization is also correct.
I mean,
d^2U/dx^2 + d^2U/dy^2 = -f,
is transformed as,
(-m^2-n^2)U'_m,n = -f'_m,n.

Then, inverse transforming for above equation must return correct result.
However, no correct answer is obtained.

What is missing in the second approach?
And how I can solve it?

Thanks in advance.
yohey44 is offline   Reply With Quote

Reply

Thread Tools
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 On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Calculation of the Governing Equations Mihail CFX 7 September 7, 2014 06:27
Poisson equation combined with transport equation Se-Hee CFX 0 December 27, 2007 02:00
Poisson Equation in CFD Maciej Matyka Main CFD Forum 9 November 10, 2004 12:30
Poisson equation vs continuity equation DJ Main CFD Forum 1 August 5, 2004 20:01
Poisson equation with Neumann boundary conditions cregeo Main CFD Forum 8 July 26, 2004 04:58


All times are GMT -4. The time now is 15:40.