A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions and in the meantime prevent spurious oscillations on solving hyperbolic conservation laws with long output times. Our goal in this article is to address this widely concerned problem [3, 4, 15, 29, 16, 18]. We firstly ] take a closer look at the mappings of various existing mapped WENO schemes and devise a general formula for them. It helps us to extend the order-preserving (OP ) criterion , originally defined and carefully examined in 18%DIFDELCMD < ]%%% , into the design of the mappings.Next , we propose the  implementation of obtaining the new mappings satisfying the OP criterion from those of the existing mapped WENO-X schemes  where the notation "X" is used to identify the version of the existing mapped WENO scheme , e. g., X = M 11%DIFDELCMD < ]%%% , PM6 3%DIFDELCMD < ]%%% , or PPM5 15%DIFDELCMD < ]%%% , et al. Then we build the resultant mapped WENO schemes and denote them as MOP-WENO-X . The numerical solutions of the one-dimensional linear advection equation with different initial conditions and some standard numerical experiments of two-dimensional Euler system, computed by the MOP-WENO-X schemes , are compared with the ones generated by their corresponding WENO-X schemes and the WENO-JS scheme. To summarize, the MOP-WENO-X schemes gain definite advatages in terms of attaining high resolutions and meanwhile avoiding spurious oscillations near discontinuities for long output time simulations of the one-dimensional linear advection problems, as well as significantly reducing the post-shock oscillations in the simulations of the two-dimensional steady problems with strong shock waves .
A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions and in the meantime prevent spurious oscillations on solving hyperbolic conservation laws with long output times. Our goal in this article is to address this widely concerned problem [3, 4, 15, 29, 16, 18]. In our previous work 18], the order-preserving (OP) criterion was originally introduced and carefully used to devise a new mapped WENO scheme that performs satisfactorily in long-run simulations, and hence it was indicated that the OP criterion plays a critical role in the maintenance of low-dissipation and robustness for the mapped WENO schemes. Thus, in our present work, we firstly define the family of the mapped WENO schemes, whose mappings meet the OP criterion, as OP-Mapped WENO. Next, we attentively take a closer look at the mappings of various existing mapped WENO schemes and devise a general formula for them. It helps us to extend the %DIFDELCMD < ]%%% OP criterion into the design of the improved mappings. Then , we propose the generalized implementation of obtaining a group of OP-Mapped WENO schemes, named MOP-WENO-X as they are developed from the existing mapped WENO-X schemes , where the notation "X" is used to identify the version of the existing mapped WENO scheme %DIFDELCMD < ]%%% %DIFDELCMD < ]%%% %DIFDELCMD < ]%%% . Finally, extensive numerical experiments and comparisons with competing schemes are conducted to demonstrate the enhanced performances of the MOP-WENO-X schemes .
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, the order-preserving (OP) criterion was originally introduced and carefully used to devise a new mapped WENO scheme that performs satisfactorily in long-run simulations, and hence it was indicated that the OP criterion plays a critical role in the maintenance of low-dissipation and robustness for the mapped WENO schemes. Thus, in our present work, we firstly define the family of the mapped WENO schemes, whose mappings meet the OP criterion, as OP-Mapped WENO. Next, we attentively
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. The numerical solutions of the one-dimensional linear advection equation with different initial conditions and some standard numerical experiments of two-dimensional Euler system, computed by the MOP-WENO-X schemes , are compared with the ones generated by their corresponding WENO-X schemes and the WENO-JS scheme. To summarize, the MOP-WENO-X
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gain definite advatages in terms of attaining high resolutions and meanwhile avoiding spurious oscillations near discontinuities for long output time simulations of the one-dimensional linear advection problems, as well as significantly reducing the post-shock oscillations in the simulations of the two-dimensional steady problems with strong shock waves