Adv. Appl. Math. Mech., 16 (2024), pp. 980-1008.
Published online: 2024-05
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In this paper, a new high-resolution WENO-MIM scheme that can achieve optimal accuracy at high-order critical points is developed. The nonlinear weight function of the new scheme can be obtained by adding a freely adjustable term with a parameter $λ$ to the mapping function of the WENO-IM scheme. A sufficient condition shows the shock-capturing ability of WENO-MIM will be enhanced with the increase of $λ.$ The parameter $λ=467$ obtained from experience can guarantee the new scheme achieves high resolution. Numerical example results show that the present scheme can achieve optimal accuracy at high-order critical points and perform significantly better than other WENO schemes in highly efficient computing of various compressible fluid problems.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0321}, url = {http://global-sci.org/intro/article_detail/aamm/23119.html} }In this paper, a new high-resolution WENO-MIM scheme that can achieve optimal accuracy at high-order critical points is developed. The nonlinear weight function of the new scheme can be obtained by adding a freely adjustable term with a parameter $λ$ to the mapping function of the WENO-IM scheme. A sufficient condition shows the shock-capturing ability of WENO-MIM will be enhanced with the increase of $λ.$ The parameter $λ=467$ obtained from experience can guarantee the new scheme achieves high resolution. Numerical example results show that the present scheme can achieve optimal accuracy at high-order critical points and perform significantly better than other WENO schemes in highly efficient computing of various compressible fluid problems.