  We present a robust, highly accurate, and efficient positivity- and
boundedness-preserving diffuse interface method for the simulations of
compressible gas-liquid two-phase flows with the five-equation model by Allaire
et al. using high-order finite difference weighted compact nonlinear scheme
(WCNS) in the explicit form. The equation of states of gas and liquid are given
by the ideal gas and stiffened gas laws respectively. Under a mild assumption
on the relative magnitude between the ratios of specific heats of the gas and
liquid, we can construct limiting procedures for the fifth order
incremental-stencil WCNS (WCNS-IS) with the first order Harten-Lax-van Leer
contact (HLLC) flux such that positive partial densities and squared speed of
sound can be ensured in the solutions, together with bounded volume fractions
and mass fractions. The limiting procedures are discretely conservative for all
conservative equations in the five-equation model and can also be easily
extended for any other conservative finite difference or finite volume scheme.
Numerical tests with liquid water and air are reported to demonstrate the
robustness and high accuracy of the WCNS-IS with the positivity- and
boundedness-preserving limiters even under extreme conditions.
