Given the Euler equations in two dimensions in a moving reference frame:(adsbygoogle = window.adsbygoogle || []).push({});

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

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[tex]

U = \left(\rho , \rho u , \rho v , \rho e \right)

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[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)

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[tex]

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

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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)

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and

[tex]

EV1=\left(0,1,0,0\right)\ ,\ EV2=\left(0,0,0,1\right)

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[tex]

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

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[tex]

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

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where

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a=\sqrt{\gamma\frac{p}{\rho}

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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?

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# Odd result from an eigenvalue problem in the Euler equations

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