(untitled) (Journal of Mathematical Study, 2017)
In this paper, we investigate the performance of a class of the hybrid weighted essentially non-oscillatory (WENO) schemes with Lax-Wendroff time discretization procedure using different indicators for hyperbolic conservation laws. The main idea of the scheme is to use some efficient and reliable indicators to identify discontinuity of solution, then reconstruct numerical flux by WENO approximation in discontinuous regions and up-wind linear approximation in smooth regions, hence reducing computational cost but still maintaining non-oscillatory properties for problems with strong shocks. Numerical results show that the efficiency and robustness of the hybrid WENO-LW schemes.