Upwind solvers for 1D compressible Euler eqns
 

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?

Something like this?
 

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

hi all.i need computer programme for solving 1D euler EQUATİONS van leer and roe scheme.plz help me