Abstract
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 \(L^1\)-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.
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Acknowledgments
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.
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Kim, C.H., Ha, Y. & Yoon, J. Modified Non-linear Weights for Fifth-Order Weighted Essentially Non-oscillatory Schemes. J Sci Comput 67, 299–323 (2016). https://doi.org/10.1007/s10915-015-0079-3
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DOI: https://doi.org/10.1007/s10915-015-0079-3