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Upwind solvers for 1D compressible Euler eqns

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Old   March 11, 2010, 14:39
Default Upwind solvers for 1D compressible Euler eqns
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I am an introductory student in CFD. I ma solving 1D Euler equations in non-conservative form. I am able to calculate the eigenvalues and eigenvector matrix. I get eigenvalues of u, u+c, and u-c. I need to find F+ and F-. I am trying to understand the Steger-Warming and Van Leer flux splitting methods. I am having trouble figuring out how to do the Steger-Warming and Van Leer. There is no info on these schemes in Wiki. Can someone explain these simply or provide an example of them in use?
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Old   March 11, 2010, 18:31
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Here describes Van Leer's splitting.
http://chimeracfd.com/programming/gr...uxvanleer.html

The Steger-Warming splitting is simple.
For the Euler equations, we have

F = AU

where F is the flux, U is the conservative state vector, and
A is the Jacobian (dF/dU)! Yes, that's true for the Euler.
So, if we decompose A into a positive part and negative part:

A = RDL = R(Dp + Dm)L = RDpL + RDmL = Ap + Am,

where R is the right-eigenvector matrix, D is the diagonal matrix with eigenvalues in the diagonal, L is the left-eigenvector (inverse of R), and
Dp is D with positive eigenvalues only, Dm is D with only negative eigenvalues, THEN we can write the flux vector as

F = Fp + Fm = ApU + AmU

So, the positive flux is ApU and the negative flux is AmU!

There is a source code for Van Leer's flux and the Steger-Warming flux at
http://www.ossanworld.com/cfdbooks/cfdcodes.html

Good luck.
gory
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Old   May 1, 2010, 04:19
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hi all.i need computer programme for solving 1D euler EQUATİONS van leer and roe scheme.plz help me
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