A General Improvement in the WENO-Z-Type Schemes

A new type of finite volume WENO schemes for hyperbolic problems was devised in [36] by introducing the order-preserving (OP) criterion. In this continuing work, we extend OP criterion to WENO-Z-type schemes. We firstly rewrite formulas Z-type weights a uniform form from mapping perspective inspired extensive numerical observations. Accrodingly, build concept locally (LOP) which is an extension and resultant improved are denoted as LOP-GMWENO-X. There four major advantages LOP-GMWENO-X superior existing Firstly, can amend serious drawback that most them suffer either producing severe spurious oscillations or failing obtain high resolutions long calculations with discontinuities. Secondly, they maintain considerably on solving high-order critical points at output times. Thirdly, evidently higher resolution region high-frequency but smooth waves. Finally, significantly decrease post-shock simulations some 2D strong shock Extensive benchmark examples conducted illustrate these advantages.