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August 12, 2010, 10:14 
Eigenvaluesand eigenvector of Euler equations 2 D

#1 
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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! 

August 12, 2010, 13:04 

#2 
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Hello,
check the book of Hirsch  Numerical computation of internal and external flows Do 

August 12, 2010, 13:06 

#3 
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Or google "eigenvectors for euler equations"  I got lots of hits that can provide that information.


August 12, 2010, 13:49 
Thanks Do,

#4 
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Miguel Caro
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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 HighResolution ShockCapturing 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 

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 multidimensional Riemann solvers are much harder to come up with than onedimensional 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.


August 13, 2010, 21:49 

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August 14, 2010, 09:53 
I will read it

#7 
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Miguel Caro
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Hi Praveen, i will read it
Thanks 

August 24, 2010, 13:00 
I found the eigenvalues and eigenvector for EUlers 2D

#8 
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Miguel Caro
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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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