second order scheme problem
 

Hi every one,
I'm solving a shock tube problem using a Roe scheme (structured grids) which works fine on first order accuracy. I want to improve the solution to higher order starting from second order.
I simply extrapolate the solution from the cell centers to faces using the gradients:

Uface=Ucenter+Grad_U*r

where r is the distance between the face and center. using this second order Taylor series I manage to improve the solution in the expansion region but the shock capturing is exactly the same as the first order solution. I use a MidMode slope limiter for the second order solution. I can's see where the problem is.
any experiences?

1) to see the quantitative difference from first and second order methods you need to do a study on the convergence slope on a smooth solution
2) A limiter reduces to first order the scheme near the shock.

I suggest to check first a difference test to see if for a regular solution your second order code is correct.

Thanks a lot Filippo,
Testing on a smooth solution is a good idea.
I quite agree that the limiter returns the solution to the first order near the shock but I can't see even a small improvement.
A second order scheme should capture a sharper shock.

First, check the convergence for a smooth solution to assess that you coded correctly the second order scheme.
Then, check the number of cells involved by the shock and check if refining the grid the shock layer width is reduced on the same number of cells.