A pragmatic approach for enhancement of the weighted essentially non-oscillatory scheme based on local Mach number

Abstract

In this work, we show that the increase of the contribution of the substencils in WENO schemes is related to local Mach number leading to less dissipative results. To this end, the general propositions in the work conducted by Acker et al. (2016) are directed. We have followed the reasoning line that the contributions to the substencil, where the solution is less smooth, are more relevant than improving the accuracy at critical points. In doing so, we propose that λ∼Ma, where Ma is the local Mach number. The new scheme effectively increased the weight of less smooth sub-stencils and led to better results for one-dimensional numerical experiments. For the Riemann problem cases (2D simulations), there seem to be unexpected oscillations and a break of symmetry. On the other hand, as far as the Shock Entropy problem (2D simulations) is concerned, the proposed scheme outperformed the WENO-Z+ formulation.