WENO - Basic Question

Graham

I am studying the WENO scheme as presented in the D S Balsara and C-W Shu paper: "Mononicity Preserving Essentially Non-oscillatory Schemes with Increasingly High Order Accuracy", JCP, 160, (2000).

Most of the ideas are fairly straight forward, and I have been able to successfully implement various order schemes in Matlab that work fine for single 1D hypebolic problems and also that solve the Euler Equations.

My question is: How are the smoothness indicator coefficients calculated. I am obviously missing something and would be interested in a step-by-step explanation.

Any help would be much appreciated.