A weighted ENO-flux limiter scheme for hyperbolic conservation laws

Abstract

We present a new scheme that combines essentially non-oscillatory (ENO) reconstructions together with monotone upwind schemes for scalar conservation laws interpolants. We modify a second-order ENO polynomial by choosing an additional point inside the stencil in order to obtain the highest accuracy when combined with the Harten–Osher reconstruction-evolution method limiter. Numerical experiments are done in order to compare a weighted version of the hybrid scheme to weighted essentially non-oscillatory (WENO) schemes with constant Courant–Friedrichs–Lewy number under relaxed step size restrictions. Our results show that the new scheme reduces smearing near shocks and corners, and in some cases it is more accurate near discontinuities compared with higher-order WENO schemes. The hybrid scheme avoids spurious oscillations while using a simple componentwise extension for solving hyperbolic systems. The new scheme is less damped than WENO schemes of comparable accuracy and less oscillatory than higher-order WENO schemes. Further experiments are done on multi-dimensional problems to show that our scheme remains non-oscillatory while giving good resolution of discontinuities.

Keywords:

• essentially non-oscillatory methods
• MUSCL-type interpolants
• UNO limiter
• multistep schemes
• hyperbolic conservation laws

2010 AMS Subject Classifications :

• 65M08
• 35L65

Acknowledgements

The authors thank the anonymous referees whose comments improved our work and the presentation of this paper. The research of A.A.I. Peer was supported by a postgraduate research scholarship from the Tertiary Education Commission and the University of Mauritius.