Closed Form Formula for WENO Smoothness Indicators with Arbitrary Order

In this article, we present a general closed form formula for computing lower order local smoothness indicators used in forming nonlinear WENO weights of arbitrary orders 2r − 1. The closed form formula of the smoothness indicators is given in a convenient matrix form. The smoothness indicators can be derived for any order of the WENO scheme through a recursive formula. A Maple code used in deriving the necessary coefficients of the lower order polynomials are also presented so that users can regenerate the necessary coefficients on their own