Modified Non-linear Weights for Fifth-Order Weighted Essentially Non-oscillatory Schemes
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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.
KeywordsHyperbolic conservation laws Euler equation WENO scheme Approximation order Smoothness indicator
Mathematics Subject Classification65M12 65M70 41A10
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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