  In this paper, we develop a simplified hybrid weighted essentially
non-oscillatory (WENO) method combined with the modified ghost fluid method
(MGFM) [28] to simulate the compressible two-medium flow problems. The MGFM can
turn the two-medium flow problems into two single-medium cases by defining the
ghost fluids status in terms of the predicted the interface status, which makes
the material interface "invisible". For the single medium flow case, we adapt
between the linear upwind scheme and the WENO scheme automatically by
identifying the regions of the extreme points for the reconstruction polynomial
as same as the hybrid WENO scheme [50]. Instead of calculating their exact
locations, we only need to know the regions of the extreme points based on the
zero point existence theorem, which is simpler for implementation and saves
computation time. Meanwhile, it still keeps the robustness and has high
efficiency. Extensive numerical results for both one and two dimensional
two-medium flow problems are performed to demonstrate the good performances of
the proposed method.
