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

what does this mean? \nabla ^3U

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

Like Tree1Likes
  • 1 Post By triple_r

Reply
 
LinkBack Thread Tools Display Modes
Old   October 13, 2013, 20:50
Default what does this mean? \nabla ^3U
  #1
Senior Member
 
Dongyue Li
Join Date: Jun 2012
Location: Torino, Italy
Posts: 667
Rep Power: 8
sharonyue is on a distinguished road
\begin{array}{l}
{\nabla ^3}U = ?\\
{\nabla ^2}U = \nabla  \cdot \nabla U
\end{array}

Thanks.
sharonyue is offline   Reply With Quote

Old   October 16, 2013, 13:37
Default
  #2
Member
 
Reza
Join Date: Mar 2009
Location: Appleton, WI
Posts: 99
Rep Power: 8
triple_r is on a distinguished road
It should mean:

\nabla^3U=\nabla\bullet\nabla^2U=\nabla\bullet\nabla\bullet\nabla U

Where did you see this term?

Last edited by triple_r; October 16, 2013 at 13:37. Reason: formatting the equation correctly
triple_r is offline   Reply With Quote

Old   October 16, 2013, 20:20
Default
  #3
Senior Member
 
Dongyue Li
Join Date: Jun 2012
Location: Torino, Italy
Posts: 667
Rep Power: 8
sharonyue is on a distinguished road
Quote:
Originally Posted by triple_r View Post
It should mean:

\nabla^3U=\nabla\bullet\nabla^2U=\nabla\bullet\nabla\bullet\nabla U

Where did you see this term?
Thanks,

You mean its a scalar rite? Actually its a simple version of the regular one. Its an equation of a turbulence model.

"Partial-average-based equations of incompressible turbulent flow"

I attach a image. This equation is tough to handle. Right now I have no idea how to solve this equation.
Attached Images
File Type: jpg 1.jpg (16.3 KB, 13 views)
sharonyue is offline   Reply With Quote

Old   October 17, 2013, 09:15
Default
  #4
Member
 
Jonas T. Holdeman, Jr.
Join Date: Mar 2009
Location: Knoxville, Tennessee
Posts: 90
Rep Power: 8
Jonas Holdeman is on a distinguished road
It could also be interpreted as a tensor \nabla(\nabla^2 U)
Jonas Holdeman is offline   Reply With Quote

Old   October 17, 2013, 11:09
Default
  #5
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,581
Rep Power: 20
FMDenaro will become famous soon enough
Quote:
Originally Posted by sharonyue View Post
Thanks,

You mean its a scalar rite? Actually its a simple version of the regular one. Its an equation of a turbulence model.

"Partial-average-based equations of incompressible turbulent flow"

I attach a image. This equation is tough to handle. Right now I have no idea how to solve this equation.

I think is a simbolic power of the operator l.Grad therefore it must be applied n times on the function
FMDenaro is offline   Reply With Quote

Old   October 18, 2013, 10:30
Default
  #6
Member
 
Reza
Join Date: Mar 2009
Location: Appleton, WI
Posts: 99
Rep Power: 8
triple_r is on a distinguished road
Ignore my first answer please, I didn't see the dot product with l. As Filippo said, it is equal to application of \ell\cdot\nabla n times in a row, and because of the dot product, it is a scalar operator.
FMDenaro likes this.
triple_r 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
libOpenSMOKE Tobi OpenFOAM Programming & Development 496 Yesterday 02:41
InterFoam: Add an equation to only one phase voingiappone OpenFOAM Programming & Development 31 December 2, 2014 10:02
modelling Differential equations in a udf RikardMNorén Fluent UDF and Scheme Programming 2 October 1, 2013 03:36
Equilibrium thru Interface hfsf OpenFOAM 5 June 28, 2013 02:55
Problem with trimmed cells when calculating \nabla \cdot \nabla \cdot (U^TU) nikwin OpenFOAM 10 August 14, 2009 04:19


All times are GMT -4. The time now is 00:12.