Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Odd result from an eigenvalue problem in the Euler equations

  1. Aug 3, 2010 #1
    Given the Euler equations in two dimensions in a moving reference frame:

    [tex]
    \frac{\partial U}{\partial t} + \frac{\partial F\left(U\right)}{\partial x} = 0
    [/tex]

    [tex]
    U = \left(\rho , \rho u , \rho v , \rho e \right)
    [/tex]

    [tex]
    F\left(U\right) = \left(\left(1-h\right)\rho u , \left(1-h\right)\rho u^2 + p , \left(1-h\right)\rho u v , \left(1-h\right)\rho u e + u p \right)
    [/tex]

    [tex]
    p = \left(\gamma -1\right)\rho \left(e-\frac{1}{2}\left(u^2+v^2\right)\right)
    [/tex]

    Where h accounts for relative motion, the eigenvalues and eigenvectors of the system are reported to be

    [tex]
    \Lambda = \left(\left(1-h\right) u,\left(1-h\right) u, \left(1-h\right)u+a,\left(1-h\right)u-a\right)
    [/tex]

    and

    [tex]
    EV1=\left(0,1,0,0\right)\ ,\ EV2=\left(0,0,0,1\right)
    [/tex]

    [tex]
    EV3=\left(\frac{1}{a^2},1,\frac{1}{\rho a} ,0\right)
    [/tex]

    [tex]
    EV4=\left(\frac{1}{a^2},1,-\frac{1}{\rho a} ,0\right)
    [/tex]

    where

    [tex]
    a=\sqrt{\gamma\frac{p}{\rho}
    [/tex]

    I have tried to reproduce this, and I've also tried to reverse it, but I'm not having any luck. Is this reported result just wrong? or am I missing something simple?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Odd result from an eigenvalue problem in the Euler equations
  1. Eigenvalue problem (Replies: 14)

  2. Euler equation (Replies: 1)

  3. Odd Elliptic equation (Replies: 7)

Loading...