讲座内容：

High-order weighted essentially non-oscillatory (WENO) schemes have been widely recognized as effective tools for solving hyperbolic conservation laws involving complex flow features such as shocks, contact discontinuities, and small-scale structures. However, their practical application in large-scale engineering problems is often hindered by substantial computational costs arising from local characteristic decompositions, smoothness indicator and nonlinear weight calculations—especially in smooth flow regions where such sophisticated treatments are unnecessary. To address this fundamental challenge, this work presents a systematic development of high-order hybrid multi-resolution WENO (HMR-WENO) schemes and modified multi-resolution WENO (MMR-WENO) schemes across multiple dimensions and mesh types, including structured grids, triangular grids, and tetrahedral grids. The core innovation lies in the design of novel troubled cell indicators that automatically identify discontinuous regions without introducing any problem-dependent parameters.