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

Gradients.

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

Reply
 
LinkBack Thread Tools Display Modes
Old   February 24, 2005, 11:30
Default Gradients.
  #1
J. Ca
Guest
 
Posts: n/a
Hi all,

Can anyone tell me how to calculate the angle between the gradient of a scalar field and a vector field in general curvilinear cordinates. Cheers.
  Reply With Quote

Old   February 24, 2005, 15:06
Default Re: Gradients.
  #2
Runge_Kutta
Guest
 
Posts: n/a
Well, first you have to decide how you have represented the two vectors; as contravariant or covariant vectors. Also, you need your metric tensor. So, for

n^{i} = nabla(scalar)

v^{j} = vector

n^{i}g_{ij}v^{j} = Sqrt(n^{i}g_{ij}n^{j})*Sqrt(n^{i}g_{ij}n^{j}) Cos(theta)

or

n_{i} = nabla(scalar)

v_{j} = vector

n_{i}g^{ij}v_{j} = Sqrt(n_{i}g^{ij}n_{j})*Sqrt(n_{i}g^{ij}n_{j}) Cos(theta)

You could also use physical components.
  Reply With Quote

Old   February 25, 2005, 07:27
Default Re: Gradients.
  #3
J. Ca
Guest
 
Posts: n/a
Thank you Runge_Kutta. What is the g^{ij} you use in your notation above? Also, can you give me a simple intepretation of what the terms covariant and contravariant mean, particularly as applied to vectors. I am having difficulty understanding books when they try to explain this.
  Reply With Quote

Old   February 25, 2005, 14:04
Default Re: Gradients.
  #4
Runge_Kutta
Guest
 
Posts: n/a
g^{ij} is the inverse of g_{ij} - the metric tensor.

A year ago, I could have said something intellegent about covariant and contravariant quantities but I'm not going to post my fuzzy recollections on this board. Sorry!
  Reply With Quote

Old   February 25, 2005, 15:11
Default Re: Gradients.
  #5
J. Ca
Guest
 
Posts: n/a
Thank you. Yes, I am empatize with you!
  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
Output of velocity gradients wersoe OpenFOAM Programming & Development 10 March 31, 2014 20:57
Velocity Gradients or Pressure Gradients? owayz OpenFOAM 9 August 14, 2012 13:09
Large pressure gradients = anisotropy??? cfd_enthusiast Main CFD Forum 0 February 9, 2010 12:09
density gradients in CFX post prabhu CFX 1 June 12, 2006 06:47
extract velocity gradients with cfx4.2 franco belosi CFX 1 November 28, 2002 19:41


All times are GMT -4. The time now is 22:42.