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Eigenvaluesand eigenvector of Euler equations 2 D

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Old   August 12, 2010, 10:14
Default Eigenvaluesand eigenvector of Euler equations 2 D
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Miguel Caro
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Hi everybody,
Pleas does anybody have the eigenvalues and eigenvetors of the Euler equations 2D?

Thanks!
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Old   August 12, 2010, 13:04
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Hello,

check the book of Hirsch - Numerical computation of internal and external flows

Do
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Old   August 12, 2010, 13:06
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Or google "eigenvectors for euler equations" - I got lots of hits that can provide that information.
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Old   August 12, 2010, 13:49
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Thanks again, i checked the book and did not find it.

But searching on the Web, i found an article of Cong Yu, "An efficient High-Resolution Shock-Capturing Scheme for Multidimensional Flows", where are written the eigenvalues and eigenvectors of the Euler equations 2D. Well, i wish to find any book of article where would be more explicit the process of calculate the eigenvector and eigenvalues.

Thanks Do again for your answer
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Old   August 13, 2010, 10:39
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The eigenvalues and eigenvectors are found using the standard process form linear algebra for the system Ax = lambda*x. In the case of the 2D euler equations you will actually have two matrices, which are the Jacobians that arise from recasting the equations from conservative form dq/dt + dE/dx + dF/dy = 0 into the quasilinear form dq/dt + A*dq/dx + B*dq/dy. Both A and B have their own eignevalues and eigenvectors, which is why you can't diagonalize the entire equation and decouple the system (and why multi-dimensional Riemann solvers are much harder to come up with than one-dimensional solvers). Once you have A and B, then solve the characteristic equation det(A - lambda*I) = 0 for the eigenvalues of A (similar for B), and then solve Ax = lambda*x for the eigenvectors of A (similar for B). It's tedious but straightforward.
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Old   August 13, 2010, 21:49
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This may help

http://aero-comlab.stanford.edu/Pape...en_gas_dyn.pdf
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Old   August 14, 2010, 09:53
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Hi Praveen, i will read it

Thanks
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Old   August 24, 2010, 13:00
Default I found the eigenvalues and eigenvector for EUlers 2D
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The people can find the eigenvalues and the eigenvectors of the Euler equations 2D handly but in this article are yet calculated

An interface tracking method for hyperbolic
systems of conservation laws
Stephen F. Davis ,1992

Thanks everybody who involve with some suggest in this question.

Thanks !
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