WENO & flux split
 

For Euler systems, the flux F(j+1/2) are usually approximated in the local characteristic fields by Roe's average matrix. First, I split f(u) into two parts locally by Lax-friedrich splitting, but I found when I used the eigenvectors at (j+1/2) to project the numerical flux, it was not convergent and when I used eigenvectors at (j), it was better than befor but the convergences rate is still poor. I don't know why. Who can give me some advice?