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

discretization of a gradient term in FVM

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

Reply
 
LinkBack Thread Tools Display Modes
Old   December 17, 2012, 11:42
Default discretization of a gradient term in FVM
  #1
Member
 
Join Date: Jun 2010
Posts: 98
Rep Power: 7
Hooman is on a distinguished road
Hi,

In the finite volume method, are there any other ways of discretizing a dv/dx term other than central differencing i.e. for instance
(dv/dx) at east face = (v_E - v_p )/(x_E -x_p ),
where p and E are the central and east nodes of a structured grid.
I am looking for a method of the same order as the CDS method above.

Thanks!
Hooman is offline   Reply With Quote

Old   December 17, 2012, 13:49
Default
  #2
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,645
Rep Power: 23
FMDenaro will become famous soon enough
Quote:
Originally Posted by Hooman View Post
Hi,

In the finite volume method, are there any other ways of discretizing a dv/dx term other than central differencing i.e. for instance
(dv/dx) at east face = (v_E - v_p )/(x_E -x_p ),
where p and E are the central and east nodes of a structured grid.
I am looking for a method of the same order as the CDS method above.

Thanks!
I think that you are focusing on an issue that is often misleading in the cfd community...

If you use FV approach, then you must discretize the surface integral of the normal component of the flux. That means:

Integral [S] n . Grad f dS

can be written in a FV manner, for example on a 2D structured Cartesian grid as:

Int [-dy/2, + dy/2] (df/dx_i+1/2 - df/dx_i-1/2) dy +
Int [-dx/2, + dx/2] (df/dy_j+1/2 - df/dy_j-1/2) dx

Now you can discretize the integral with the mean value formula and the derivative with second order central formula, getting a global second order of accuracy.
If you want to increase the accuracy, you can use the Simpon rule for the integral and a third degree polynomial interpolation for the derivatives, as we explained in http://adsabs.harvard.edu/abs/2003IJNMF..43..431I
FMDenaro is offline   Reply With Quote

Old   December 17, 2012, 13:59
Default
  #3
Member
 
Join Date: Jun 2010
Posts: 98
Rep Power: 7
Hooman is on a distinguished road
I don't want to use any higher order method that involve cells other than the neighbouring cells.
Hooman is offline   Reply With Quote

Old   December 17, 2012, 15:06
Default
  #4
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,645
Rep Power: 23
FMDenaro will become famous soon enough
Quote:
Originally Posted by Hooman View Post
I don't want to use any higher order method that involve cells other than the neighbouring cells.

ok, then you have two choice, Lagrangian linear interpolation for a second order accuracy or implicit Padè interpolation for higher
FMDenaro 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
Problem of SOURCE term gradient in UDS wind Fluent UDF and Scheme Programming 5 June 21, 2013 05:39
ATTENTION! Reliability problems in CFX 5.7 Joseph CFX 14 April 20, 2010 15:45
gradient source term UDF ak6g08 Fluent UDF and Scheme Programming 0 July 9, 2009 06:37
FVM discretization of diffusion term on crvlnr gr Michail Main CFD Forum 3 March 14, 2008 07:52
pressure gradient term in low speed flow Atit Koonsrisuk Main CFD Forum 2 January 10, 2002 11:52


All times are GMT -4. The time now is 00:30.