Before revision:  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.
After revision:  It helps us to extend the order-preserving (OP ) criterion , originally defined and carefully examined in 18 , into the design of the improved mappings. Then , 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.