Consistent and bound-preserving finite-volume WENO scheme for compressible two-/$N$-phase flows with Phase-Field mechanism

Abstract

In the present study, we propose a consistent and bound-preserving finite-volume WENO scheme that satisfies the requirements of consistency, conservation, equilibrium, and bound preservation for compressible multiphase flows with the Phase-Field mechanism. The proposed WENO scheme is developed based on a new calculation of WENO weights determined by relative smoothness between stencils and on a coupled reconstruction of the masses and volume fractions. Consistency of reduction and volume fraction summation to unity are considered during the development so that fictitious phases, local voids, or overfilling are not produced numerically when there are $N$ ($N \geqslant 1$) different immiscible phases. The proposed WENO scheme is applied to the consistent and conservative Phase-Field method with adaptive mesh refinement enabled. Various benchmark compressible two- and $N$-phase flows are performed to verify the properties of the proposed WENO scheme as well as its variant with the consistent limiter. We finally demonstrate the capability of the proposed WENO scheme in shock-induced cavity collapse and shock-vessel-bubble interaction problems, with discussion of the necessity of bound preservation for high-order schemes and comparison of different compressible multiphase flow models.