Before revision: In 18 , the authors have designed a new finite-volume mapped WENO scheme by introducing a new criterion which is defined as order-preserving (OP) in the design of the mapping. With this new criterion, a new mapping function was devised and the relevant mapped WENO scheme enjoyed the advantage that has the capacity to attain high resolutions and avoid spurious oscillations near discontinuities when solving the one-dimensional linear advection problems, expecially for long output times.
After revision: In 18 A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions and avoid spurious oscillations near discontinuities when solving the one-dimensional linear advection problems, expecially for long output times.