WENO interpolations and reconstructions using data bounded polynomial approximation

TL;DR

This paper develops data bounded polynomial-based WENO interpolations that maintain high accuracy for smooth functions and prevent oscillations near discontinuities and extrema.

Contribution

It introduces data bounded conditions for third and fourth order WENO weights, enhancing stability and accuracy in WENO schemes.

Findings

Achieves high accuracy for smooth functions

Prevents overshoot and undershoot near discontinuities

Proposes high order data-bounded WENO schemes

Abstract

This work characterizes the structure of third and forth order WENO weights by deducing data bounded condition on third order polynomial approximations. Using these conditions, non-linear weights are defined for third and fourth order data bounded weighted essentially non-oscillatory (WENO) approximations. Computational results show that data bounded WENO approximations for smooth functions achieve required accuracy and do not exhibit overshoot or undershoot for functions with discontinuities and extrema. Further with suitable weights, high order data-bounded WENO approximations are proposed for WENO schemes.