In this article, a new variant of third order WENO scheme is constructed based on a simple global smoothness indicator that satisfies the sufficient condition for convergence in terms of nonlinear weights. By using this simple global smoothness indicator, the proposed WENO scheme provides third order accuracy and also reduces computational cost of WENO-NP3 scheme at critical points. The issues of numerical resolution and efficiency of WENO schemes for computing numerical solutions containing both discontinuities and complex solution features are addressed. We have investigated the proposed scheme through several benchmark test cases for one-dimensional linear wave and Burger’ equations, one- and two-dimensional systems of Euler equations. Third order TVD Runge-Kutta method is applied for all considered WENO schemes. The performance of developed WENO scheme provides more accurate and efficient solutions with better resolutions than higher order WENO-JS3, WENO-Z3 and WENO-NP3 schemes.

WENO, critical points, smoothness indicator, CPU time, convergence.

Received: May 2, 2021; Revised: May 28, 2021; Accepted: June 30, 2021; Published: July 31, 2021

How to cite this article: Anurag Kumar and Bhavneet Kaur, A third order Weno scheme with a simple global smoothness indicator to improve convergence rate at critical points, JP Journal of Heat and Mass Transfer 23(2) (2021), 359-388. DOI: 10.17654/HM023020359

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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