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Modified Non-linear Weights for Fifth-Order Weighted Essentially Non-oscillatory Schemes
- Modified Non-linear Weights for Fifth-Order Weighted Essentially Non-oscillatory Schemes
- Kim, Chang Ho; Ha, Youngsoo; Yoon, Jungho
- Ewha Authors
- SCOPUS Author ID
- Issue Date
- Journal Title
- JOURNAL OF SCIENTIFIC COMPUTING
- 0885-7474; 1573-7691
- vol. 67, no. 1, pp. 299 - 323
- Hyperbolic conservation laws; Euler equation; WENO scheme; Approximation order; Smoothness indicator
- SPRINGER/PLENUM PUBLISHERS
- SCIE; SCOPUS
- 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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