Locally order-preserving mapping for WENO methods

In our previous studies (Li and Zhong, 2021a; Li 2021b), the commonly reported issue that most of existing mapped WENO schemes suffer from either losing high resolutions or generating spurious oscillations in long-run simulations hyperbolic problems has been successfully addressed, by devising improved schemes, namely MOP-WENO-X, where “X” stands for version scheme. However, all MOP-WENO-X bring about serious deficiency their region with smoothly varying high-frequency waves are dramatically decreased compared to associated WENO-X schemes. The purpose this paper is overcome drawback. We first present locally order-preserving (LOP) mapping. Then, using a new proposed posteriori adaptive technique, we apply LOP property obtain mappings those essential idea technique identify global stencil which fail preserve property, then replace weights classic WENO-JS scheme recover property. build resultant denote them as LOP-WENO-X. numerical experiments demonstrate but smooth LOP-WENO-X similar even better than naturally much higher Furthermore, gain great advantages such attaining meantime preventing near discontinuities when solving one-dimensional linear advection long output times, significantly reducing post-shock two-dimensional shock waves.