This paper is concerned with fifth-order weighted essentially non-oscillatory (WENO) scheme with a new smoothness indicator. As the so-called WENO-JS scheme (Jiang and Shu in J Comput Phys 126:202–228, 1996) provides the third-order accuracy at critical points where the first and third order derivatives do not becomes zero simultaneously, several fifth-order WENO scheme have been developed through modifying the known smoothness indicators of WENO-JS. Recently a smoothness indicator based on (Formula presented.) -norm has been proposed by Ha et al. (J Comput Phys 232:68–86, 2013) (denoted by WENO-NS). The aim of this paper is twofold. Firstly, we further improve the smoothness indicator of WENO-NS and secondly, using this measurement, we suggest new nonlinear weights by simplifying WENO-NS weights. The proposed WENO scheme provides the fifth-order accuracy, even at critical points. Some numerical experiments are provided to demonstrate that the present scheme performs better than other WENO schemes of the same order.
Bibliographical noteFunding Information:
Jungho Yoon was supported by the Grant 2015-R1A5A1009350 through the National Research Foundation of Korea (NRF). Youngsoo Ha was supported by NRF-2013R1A1A2013793 and Chang Ho Kim was by NRF-2014M1A7A1A03029872 through the National R&D Program funded by the Ministry of Education, Science and Technology.
© 2015, Springer Science+Business Media New York.
- Approximation order
- Euler equation
- Hyperbolic conservation laws
- Smoothness indicator
- WENO scheme