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], 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], PM6 [3], or PPM5 [15], 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.

翻译：在现有的已映射WENO计划中,一个严重且普遍的问题是,大多数此类方案几乎无法保存高分辨率,同时防止在用较长输出时间解决超双曲保护法时出现虚假的振荡。我们在本篇文章中的目标是解决这一广泛关切的问题[3,15,29,16,18]。我们首先更仔细地查看现有已映射WENO计划的映射图,并为它们设计一个通用公式。这帮助我们将最初在[18] 中界定和仔细审查的维持秩序(OP)标准扩大到绘图的设计中。 下一步,我们建议从现有已映射WENO-X的WENO-X计划中获取符合OP标准的新的绘制结果。 在目前绘制的WENO-X计划中,将一线-线-线-直线-直线-直线-直线-直线-直线-直线-直线-直线-直线-直线-直线-直线-直线-直线-直径对等,通过两维-维-直径的系统-直径直径的平图-直径对等-直径对等-平图,将WEX的计算-直径-直线-直径-直径-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-平-