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

Convergence criteria

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

Reply
 
LinkBack Thread Tools Display Modes
Old   August 2, 2010, 10:55
Default Convergence criteria
  #1
Senior Member
 
Join Date: Apr 2009
Posts: 118
Rep Power: 9
lost.identity is on a distinguished road
Hi,

I'm using the SIMPLER method with a certain under-relaxation factor. Initially my convergence criteria was based on L2-norm as follows

error = \frac{||R||^n_2}{N} \leq 10^{-4}

where R is the difference between the previous iteration and the current iteration. However I noticed that this criteria only gave the analytical solution when the URF=1, which I later found out that with a URF<1, it gives me false convergence as the difference between the two iteraitons is reduced.

I then decided to use the following criteria instead

error = \frac{||R||^n_2}{||R||^m_{2_{max}}} \leq 10^{-4}

where ||R||^m_{2_{max}} denotes the maximum error after m iterations. Now I seem to get the correct result, I'm just wondering is this a normal way to determine convergence for such cases?

Thanks.
lost.identity is offline   Reply With Quote

Old   August 2, 2010, 11:11
Default
  #2
Super Moderator
 
praveen's Avatar
 
Praveen. C
Join Date: Mar 2009
Location: Bangalore
Posts: 255
Blog Entries: 6
Rep Power: 10
praveen is on a distinguished road
This can be a tricky issue. Suppose you are solving Au=f using an iterative method. Then

\|u^{n+1}-u^n\|

is not a good convergence measure. A better one is

\| A u^{n+1} - f\|

but even this can be misleading if A is poorly conditioned. Assuming A is not very badly conditioned, a still better one is

\frac{ \| A u^{n+1} - f\|}{\|f\|}
praveen is offline   Reply With Quote

Old   August 2, 2010, 11:19
Default
  #3
Senior Member
 
Join Date: Apr 2009
Posts: 118
Rep Power: 9
lost.identity is on a distinguished road
Thank you very much. One of the problem is when I look at papers everyone seems to be using their own convergence criteria. Do you know of any book that explains how this is done? The Kreyszig Engineering maths book gives your first method.

I've seen a paper where it was done as (using your notation)

\frac{||u^{n+1}-u^n||}{||f||}

I think this is similar to what you gave at the end but without the coefficient matrix A being multiplied. Is it necessary to multiply it?
lost.identity is offline   Reply With Quote

Old   August 2, 2010, 11:23
Default
  #4
Super Moderator
 
praveen's Avatar
 
Praveen. C
Join Date: Mar 2009
Location: Bangalore
Posts: 255
Blog Entries: 6
Rep Power: 10
praveen is on a distinguished road
If your purpose is to solve Au=f, then it is natural to measure convergence through the difference ||Au-f|| since this measures how well the equation is satisfied by the current solution.

Dividing by ||f|| will remove scale effects.
praveen 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
What value shall I set for the Convergence criteria? steventay CFX 7 May 14, 2010 12:44
convergence criteria iuaniu CFX 3 September 24, 2009 19:20
Convergence criteria PrandtlGlawert FLUENT 1 August 13, 2009 18:06
Convergence criteria PrandtlGlawert Main CFD Forum 1 August 13, 2009 17:13
Convergence Criteria edwin FLUENT 1 February 14, 2008 20:24


All times are GMT -4. The time now is 22:53.