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Old   January 31, 2014, 04:50
Red face Math Question: 2D Euler Equations
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Wojo Woyczynski
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New to CFD and trying to understand some of the physics behind it. I'm trying to find the solution to the characteristics 2D steady state Euler equations.

If you look at the attached image, I don't understand how to get from 1 to 2. Any advice is much appreciated but please use detail and write it out if possible!

Also, for both supersonic and subsonic are the 2D Euler equations hyperbolic or elliptic? How do you prove it?

Thanks
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Old   January 31, 2014, 04:59
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Filippo Maria Denaro
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Originally Posted by g.woyczynski View Post
New to CFD and trying to understand some of the physics behind it. I'm trying to find the solution to the characteristics 2D steady state Euler equations.

If you look at the attached image, I don't understand how to get from 1 to 2. Any advice is much appreciated but please use detail and write it out if possible!

Also, for both supersonic and subsonic are the 2D Euler equations hyperbolic or elliptic? How do you prove it?

Thanks

Have a look to the Zucrow book, also the way to understand the ellipric/hyperbolic character is to introduce the potential function and study the nature (real or not) of the characteristic curves
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Old   February 1, 2014, 00:42
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Gotchya, do you know the exact title of the book?
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Old   February 1, 2014, 06:58
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Gotchya, do you know the exact title of the book?

Zucrow-Hoffman Gas Dynamics Vol.1 and 2
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Old   February 3, 2014, 10:23
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Steady State Euler Equation: It is elliptic for subsonic. Parabolic for M=1 and hyperbolic for supersonic. The proof is based on finding the eigen values of the PDE. The proof is given in most of the CFD books. You can refer CFD by Anderson.

Last edited by AshwaniAssam; February 3, 2014 at 10:24. Reason: Book name was incomplete.
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