  The majority of available numerical algorithms for interfacial two-phase
flows either treat both fluid phases as incompressible (constant density) or
treat both phases as compressible (variable density). This presents a
limitation for the prediction of many two-phase flows, such as subsonic fuel
injection, as treating both phases as compressible is computationally expensive
due to the very stiff pressure-density-temperature coupling of liquids. A
framework with the capability of treating one phase compressible and the other
phase incompressible, therefore, has a significant potential to improve the
computational performance and still capture all important physical mechanisms.
We propose a numerical algorithm that can simulate interfacial flows in all
Mach number regimes, ranging from $M=0$ to $M > 1$, including interfacial flows
in which compressible and incompressible fluids interact, within the same
pressure-based framework and conservative finite-volume discretisation. For
interfacial flows with only incompressible fluids or with only compressible
fluids, the proposed pressure-based algorithm and finite-volume discretisation
reduce to numerical frameworks that have already been presented in the
literature. Representative test cases are used to validate the proposed
algorithm, including mixed compressible-incompressible interfacial flows with
acoustic waves, shock waves and rarefaction fans.
