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In our latest studies, by introducing the novel order-preserving (OP)criterion, we have successfully addressed the widely concerned issue of thepreviously published mapped weighted essentially non-oscillatory (WENO) schemesthat it is rather difficult to achieve high resolutions on the premise ofremoving spurious oscillations for long-run simulations of the hyperbolicsystems. In the present study, we extend the OP criterion to the WENO-Z-typeschemes as the forementioned issue has also been extensively observednumerically for these schemes. Firstly, we innovatively present the concept ofthe generalized mapped WENO schemes by rewriting the Z-type weights in auniform formula from the perspective of the mapping relation. Then, wenaturally introduce the OP criterion to improve the WENO-Z-type schemes, andthe resultant schemes are denoted as MOP-GMWENO-X. Finally, extensive numericalexperiments have been conducted to demonstrate the benefits of these newschemes. We draw the conclusion that, the convergence propoties of the proposedschemes are equivalent to the corresponding WENO-X schemes. The major benefitof the new schemes is that they have the capacity to achieve high resolutionsand simultaneously remove spurious oscillations for long simulations. The newschemes have the additional benefit that they can greatly decrease thepost-shock oscillations on solving 2D Euler problems with strong shock waves.

An extension of the order-preserving mapping to the WENO-Z-type schemes