讲座内容：

Numerical study on compressible two-medium flows has been a hot issue in recent decades due to broad applications in gas bubble dynamics, underwater explosion, inertial confinement fusion, and so on. In this study, we present fifth-, seventh- and ninth-order finite difference quasi-conservative alternative WENO (AWENO) schemes with Lax-Friedrichs numerical flux for the five-equation transport model (Allaire, et. al., JCP, 2002) of two-medium flows with the stiffened gas equation of state. We propose a uniformly high order flux-based bound- and positivity-preserving (BP-P) limiters for the scheme, while preserving the equilibrium solutions simultaneously. Once the BP-P limiters are used, oscillations may be generated at material interface. To this end, we introduce the affine-invariant WENO interpolations, which take care of structures, especially in small scales. In addition, we will systematically derive the BP-P CFL conditions. Numerical examples demonstrate robustness and effectiveness of the proposed schemes.