# Eigenvaluesand eigenvector of Euler equations 2 D

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 August 12, 2010, 10:14 Eigenvaluesand eigenvector of Euler equations 2 D #1 New Member   Miguel Caro Join Date: Apr 2010 Posts: 26 Rep Power: 9 Hi everybody, Pleas does anybody have the eigenvalues and eigenvetors of the Euler equations 2D? Thanks!

 August 12, 2010, 13:04 #2 Senior Member   Join Date: Nov 2009 Posts: 411 Rep Power: 12 Hello, check the book of Hirsch - Numerical computation of internal and external flows Do

 August 12, 2010, 13:06 #3 Senior Member   Join Date: Jul 2009 Posts: 247 Rep Power: 12 Or google "eigenvectors for euler equations" - I got lots of hits that can provide that information.

 August 12, 2010, 13:49 Thanks Do, #4 New Member   Miguel Caro Join Date: Apr 2010 Posts: 26 Rep Power: 9 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

 August 13, 2010, 10:39 #5 Senior Member   Join Date: Jul 2009 Posts: 247 Rep Power: 12 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.

 August 13, 2010, 21:49 #6 Super Moderator     Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 261 Blog Entries: 6 Rep Power: 11

 August 14, 2010, 09:53 I will read it #7 New Member   Miguel Caro Join Date: Apr 2010 Posts: 26 Rep Power: 9 Hi Praveen, i will read it Thanks

 August 24, 2010, 13:00 I found the eigenvalues and eigenvector for EUlers 2D #8 New Member   Miguel Caro Join Date: Apr 2010 Posts: 26 Rep Power: 9 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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