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Linear degenerate and genenuiely nonlinear???

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Old   November 23, 2001, 09:03
Default Linear degenerate and genenuiely nonlinear???
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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?

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Old   November 23, 2001, 10:47
Default Re: Linear degenerate and genenuiely nonlinear???
Axel Rohde
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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.),

Let me know if you have any more questions!

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Old   December 26, 2013, 01:27
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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.

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Old   March 22, 2016, 02:32
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Dear Paul,

You may find some explanation in the book titled " I do like CFD,Vol 1", pages 42-43.
Below, I share the link of the same:
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