Before revision:  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 .
After revision:  Then we build the resultant mapped WENO schemes and denote them as 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 .