[krolm]

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.

[Eifoehn4]

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