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

stability condition for 4th order of CD

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

Reply
 
LinkBack Thread Tools Display Modes
Old   March 20, 2008, 22:30
Default stability condition for 4th order of CD
  #1
qunwuhe@hotmail.com
Guest
 
Posts: n/a
what is the stability condition for 4th oder of central difference for diffusion equation?

for 2th, is delta t < delta x^2 is it delta t < delta x^4?

  Reply With Quote

Old   April 20, 2008, 17:35
Default Re: stability condition for 4th order of CD
  #2
Mohamed
Guest
 
Posts: n/a
Hello ,

To get the stability condition you can perform if you are using a linear scheme ( which is obviously the case ) , a von neumann analysis, i.e., you inject a fourier in your scheme

Fourier mode : ------------

u(xj,tn) = A(k)^n *exp(2*i*pi*k*xj)

where xj = j*dx and tn = n*dt and k is the wave vector (variable in fourier space)

Stability condition : -------------------

Then the stability condition is |A(k)| < 1 . You have then to determine the relationship between dx , nu and dt to satisfy the stability condition.

It is a simple computatio that you can do by hands in 1D.

Best regards, Mohamed.
  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
Unstable flow simpleFoam 2nd order Valle OpenFOAM 0 August 26, 2009 08:12
stability and number of processors ?? sersunzo OpenFOAM Running, Solving & CFD 0 June 9, 2009 11:45
On LBB stability condition Yang Cao Main CFD Forum 1 June 21, 2006 06:10
1st order temporal & 2nd order spatial Prateep Chatterjee FLUENT 0 January 19, 2003 01:31
stability condition manfred krueger Main CFD Forum 2 March 8, 2001 14:20


All times are GMT -4. The time now is 16:58.