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• W2948257535 abstract "In this article, new efficient seventh order adaptive WENO schemes are proposed for hyperbolic conservation laws. The accuracy of proposed schemes are comparable with existing versions of seventh order adaptive WENO scheme known as WENO-AO(7,3) and WENO-AO(7,5,3) [Balsara, Garain, and Shu, J. Comput. Phys., 326 (2016), pp. 780–804]. The accuracy of the new family of WENO schemes in resolving shocks or other discontinuities and high frequency waves are better than that of WENO-AO(7,3) and WENO-AO(7,5,3) schemes on a coarse mesh. In general, WENO schemes with adaptive order have the drawback that they involve computation of an extra smoothness indicator over the bigger stencil as compared to classical WENO schemes. In order to reduce the computational cost, a new simple smoothness indicator is proposed for the bigger stencil using the information available from smoothness indicators defined over smaller stencils and it is equal to original smoothness indicator upto O(Δx6) at truncation error level. The new WENO schemes of adaptive order developed using the new smoothness indicator gives comparable solution to other WENO schemes of adaptive order. We have proved that in each WENO reconstruction of adaptive order, nonlinear weights approach the linear weights and flux converges with order of seven, when the solution is smooth over the underlying stencil S07. Extensive numerical experiments are performed in one and two dimensions to validate the present algorithms." @default.
• W2948257535 created "2019-06-14" @default.
• W2948257535 creator A5074579485 @default.
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• W2948257535 date "2019-08-01" @default.
• W2948257535 modified "2023-10-18" @default.
• W2948257535 title "Efficient seventh order WENO schemes of adaptive order for hyperbolic conservation laws" @default.
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• W2948257535 doi "https://doi.org/10.1016/j.compfluid.2019.06.003" @default.
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