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Derivatives using WENO

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Old   May 16, 2022, 09:38
Default Derivatives using WENO
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Hi,
Iíd 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. Iím using Legendre polynomials for reconstruction. However, I donít think I get the derivatives right, as some of the values seem to be wrong. Unfortunately, I havenít found any precise description how to do it. How to get the proper weights, smoothnesses indicators and polynomials? Iím 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.
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Old   May 18, 2022, 17:41
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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.

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