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The main aim of this work is not to improve any existing non-linear weightbut to give a generalized framework for the construction of non-linear weightsto get non-oscillatory third order WENO schemes. It is done by imposingnecessary conditions on weights to get non-oscillatory WENO reconstructionwhich give further insight on the structure of weights to ensure non-occurrenceof oscillations and characterize the solution region for third order accuracy.This framework for WENO weights is new and completely different from theprevailing existing approach. New non-linear weights are designed using afunction of smoothness parameter termed as weight limiter functions. Many suchweight limiter functions are given and analyzed. These new weights are simpleand by construction guarantee for exact third order accuracy in smooth solutionregion including smooth extrema away from critical point. Numerical results forvarious test problems are given and compared. Results show that proposedweights give third order accuracy without loosing the non-oscillatory shockcapturing ability of the resulting scheme.

A generalized framework to construct third order WENO weights using weight limiter functions