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

Linear degenerate and genenuiely nonlinear???

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

Reply
 
LinkBack Thread Tools Display Modes
Old   November 23, 2001, 09:03
Default Linear degenerate and genenuiely nonlinear???
  #1
Paul
Guest
 
Posts: n/a
In any elementary books about the conservation laws, we will come across the definitions of linear degenerate and genenuiely nonlinear waves. However, I never find the meaning of these two concepts, except the mathematic expressions about the eigenvalues and eigenvectors. Does any one know the meaning of these two guyes?

  Reply With Quote

Old   November 23, 2001, 10:47
Default Re: Linear degenerate and genenuiely nonlinear???
  #2
Axel Rohde
Guest
 
Posts: n/a
For further study on this topic, I highly recommend Ami Harten's original paper on TVNI (Total Variation Non-Increasing), which was later abbreviated to TVD (Total Variation Diminishing).

"High Resolution Schemes for Hyperbolic Conservation Laws" (Ami Harten)

Journal of Computational Physics, Volume 49, p.357-393, 1983

On p.374 it talks about the two waves:

"We consider here systems of conservation laws where the characteristic fields are either genuinely nonlinear (R a <> 0) or linearly degenerate (R a = 0). The waves of a genuinely non-linear field are either shocks or rarefaction waves, depending whether the waves are convergent or divergent. The waves of a linearly degenerate field are exclusively contact discontinuities."

In the above, 'R' is the matrix of right eigenvectors and 'a' is the vector of eigenvalues.

The above paper is written by a mathematician and in my opinion is pretty hard to follow. If you want to read this stuff in 'plain English', then download my dissertation, where I talk about these concepts in detail (TVD, Euler Equations, Eigensytem, etc.),

www.cfd4pc.com/papers.htm

Let me know if you have any more questions!

Axel
  Reply With Quote

Old   December 26, 2013, 01:27
Default
  #3
New Member
 
Mukkarum Hussain
Join Date: Nov 2013
Posts: 2
Rep Power: 0
Mukkarum is on a distinguished road
Dear Axel Rohde

I need your dissertation where you talk about these concept in detail (TVD, Euler Equations, Eigen sytem, etc.)

Your given link is not working.

Thanks
Mukkarum 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



All times are GMT -4. The time now is 20:02.