A modified fifth-order WENO scheme for hyperbolic conservation laws

TL;DR

This paper introduces a modified fifth-order WENO scheme that enhances accuracy at critical points by employing a new global-smoothness indicator, outperforming previous methods in hyperbolic conservation law computations.

Contribution

A novel fifth-order WENO scheme with an improved global-smoothness indicator that maintains optimal accuracy at complex critical points.

Findings

Achieves fifth-order accuracy at critical points where derivatives vanish

Outperforms existing WENO-NS and WENO-P schemes in accuracy

Maintains optimal approximation order in challenging conditions

Abstract

This paper deals with a new fifth-order weighted essentially non-oscillatory (WENO) scheme improving the WENO-NS and WENO-P methods which are introduced in Ha et al. J. Comput. Phys. (2013) and Kim et al., J. Sci. Comput. (2016) respectively. These two schemes provide the fifth-order accuracy at the critical points where the first derivatives vanish but the second derivatives are non-zero. In this paper, we have presented a scheme by defining a new global-smoothness indicator which shows an improved behavior over the solution to the WENO-NS and WENO-P schemes and the proposed scheme attains optimal approximation order, even at the critical points where the first and second derivatives vanish but the third derivatives are non-zero.