A high-efficiency and low-dissipation hybrid weighted essentially   non-oscillatory scheme
  In this paper, we propose a simple hybrid WENO scheme to increase computational efficiency and decrease numerical dissipation. Based on the characteristic-wise approach, the scheme switches the numerical flux of each characteristic variables between that of WENO scheme and its optimal linear scheme according to a discontinuity detector measuring the non-resolvability of the linear scheme. A number of numerical examples computed with 5th-order WENO scheme suggested that, while achieving very small numerical dissipation and good robustness, the computational effort on WENO flux used in the hybrid scheme is negligible. 
X. Y. Hu, B. Wang and N. A. Adams
physics.flu-dyn