An efficient low-dissipation hybrid weighted essentially non-oscillatory scheme

In this paper we propose a simple hybrid WENO scheme that has improved computational efficiency and less numerical dissipation compared to previous approaches. Based on the characteristic-decomposition approach, the scheme switches between numerical fluxes with characteristic-wise WENO reconstruction and with component-wise corresponding optimal linear reconstruction according to a new discontinuity detector. This non-dimensional discontinuity detector measures the local resolution limit of the linear scheme and does not degenerate at critical points. A number of numerical examples of inviscid and viscous flow problems shows that the hybrid scheme achieves small numerical dissipation and good robustness, and generally exhibits a very small amount of WENO calls.