A 3rd-Order WENO Scheme for Stencil Smoothness Indicators Based on Mapping

The key to whether the WENO scheme can achieve optimal convergence accuracy and maintain essential no-oscillation characteristics near discontinuities lies in the construction of smoothness indicators. The smoothness indicator of the 3rd-order WENO scheme was modified through the construction of a mapping function to correct the smoothness indicators on each candidate stencil with the smoothest indicator. Under the influence of this mapping function, the smoothness indicator of the under-smooth stencil was reduced, thereby the nonlinear weight of the under-smooth stencil was increased. Then the numerical dissipation of the scheme was significantly lowered and its resolution was improved. A series of numerical examples demonstrate that, the new 3rd-order WENO scheme for smoothness indicators based on mapping has higher resolution than the classical WENO-JS3 and WENO-Z3 schemes.