Derivatives using WENO
 

Hi,
I’d like to ask you for some help. Could anyone explain me how to obtain higher order derivatives (eg. up to 3rd) using WENO schemes? Preferably step by step.
I try to use higher order WENO scheme on finite volumes in my code and I think I understand this method well enough. It seems to work. I’m using Legendre polynomials for reconstruction. However, I don’t think I get the derivatives right, as some of the values seem to be wrong. Unfortunately, I haven’t found any precise description how to do it. How to get the proper weights, smoothnesses indicators and polynomials? I’m unfortunately not an expert on numerical methods.
Therefore I am here asking if you could help me and explain the procedure so I could definitely get the derivatives right?

Best regards, thanks in advance.

Generally people use precomputed numbers available from original papers. There the procedure is decribed quite well:

Essentially non-oscillatory and weighted
Very high order WENO

• The reconstruction values (relation between the polynomial representation and the integral mean representation) can easily be obtained with Gauss quadrature and interpolation matrices.
• The more tricky part is the calculation of the values for the non-linear smoothness indicator.

Regards