A revised computation is introduced to address numerical overshoots inherent in high-order (9th and 11th) weighted essentially non-oscillatory (WENO) discretizations. These artifacts, observed even in simple 1-D simulations and particularly in regions of sharp gradients, cause persistent errors that do not diminish with decreasing CFL number, thus limiting the quality of solutions. The proposed revision modifies expressions of smooth indicators, enabling straightforward integration into existing subroutines. We showcase its effectiveness through three 1-D examples: the transport equation, the inviscid Burgers' equation, and the single-column version of the anelastic convective entity model. The results significantly improves the cost–benefit of high-order WENO in geophysical applications, positioning it as a more favorable option for both limiting methods and regular spatial discretization than previously assessed.
Yi‐Hung Kuo (Fri,) studied this question.