  Multiphase, compressible and viscous flows are of crucial importance in a
wide range of scientific and engineering problems. Despite the large effort
paid in the last decades to develop accurate and efficient numerical techniques
to address this kind of problems, current models need to be further improved to
address realistic applications. In this context, we propose a numerical
approach to the simulation of multiphase, viscous flows where a compressible
and an incompressible phase interact in the low-Mach number regime. In this
frame, acoustics is neglected but large density variations of the compressible
phase can be accounted for as well as heat transfer, convection and diffusion
processes. The problem is addressed in a fully Eulerian framework exploiting a
low-Mach number asymptotic expansion of the Navier-Stokes equations. A Volume
of Fluid approach (VOF) is used to capture the liquid-gas interface, built on
top of a massive parallel solver, second order accurate both in time and space.
The second-order-pressure term is treated implicitly and the resulting pressure
equation is solved with the eigenexpansion method employing a robust and novel
formulation. We provide a detailed and complete description of the theoretical
approach together with information about the numerical technique and
implementation details. Results of benchmarking tests are provided for five
different test cases.
