A hybrid method for improving the robustness of WENO scheme

In this paper, a hybrid scheme based on fifth-order finite difference WENO scheme is proposed for solving spurious oscillation in strong shock-capturing. In this scheme, we consider smoothness indicator as a measurement of gradient and construct a function of indicator, using which the new hybrid can switch between WENO scheme and Lax-Friedrichs (LxF) scheme. Numerical experiments demonstrate that the hybrid scheme dominates the accuracy of the solution in smooth region and non-oscillation can be promised around discontinuity. The new hybrid scheme could essentially preserve positive density and positive pressure. The idea of constructing the hybrid can be easily extended to other high resolution schemes (TVD, ROE etc.) coupled with WENO scheme. These ideas will be illustrated in further study.