Adv. Appl. Math. Mech., 15 (2023), pp. 202-243.
Published online: 2022-10
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In the present study, we extend the order-preserving (OP) criterion proposed in our latest studies to the WENO-Z-type schemes. Firstly, we innovatively present the concept of the generalized mapped WENO schemes by rewriting the Z-type weights in a uniform formula from the perspective of the mapping relation. Then, we naturally introduce the OP criterion to improve the WENO-Z-type schemes, and the resultant schemes are denoted as MOP-GMWENO-X, where the notation “X” is used to identify the version of the existing WENO-Z-type scheme in this paper. Finally, extensive numerical experiments have been conducted to demonstrate the benefits of these new schemes. We draw the conclusion that, the convergence properties of the proposed schemes are equivalent to the corresponding WENO-X schemes. The major benefit of the new schemes is that they have the capacity to achieve high resolutions and simultaneously remove spurious oscillations for long simulations. The new schemes have the additional benefit that they can greatly decrease the post-shock oscillations on solving 2D Euler problems with strong shock waves.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0032}, url = {http://global-sci.org/intro/article_detail/aamm/21132.html} }In the present study, we extend the order-preserving (OP) criterion proposed in our latest studies to the WENO-Z-type schemes. Firstly, we innovatively present the concept of the generalized mapped WENO schemes by rewriting the Z-type weights in a uniform formula from the perspective of the mapping relation. Then, we naturally introduce the OP criterion to improve the WENO-Z-type schemes, and the resultant schemes are denoted as MOP-GMWENO-X, where the notation “X” is used to identify the version of the existing WENO-Z-type scheme in this paper. Finally, extensive numerical experiments have been conducted to demonstrate the benefits of these new schemes. We draw the conclusion that, the convergence properties of the proposed schemes are equivalent to the corresponding WENO-X schemes. The major benefit of the new schemes is that they have the capacity to achieve high resolutions and simultaneously remove spurious oscillations for long simulations. The new schemes have the additional benefit that they can greatly decrease the post-shock oscillations on solving 2D Euler problems with strong shock waves.