  We present a novel pressure-based method for weakly compressible multiphase
flows, based on a non-equilibrium Baer and Nunziato-type model. In this work,
we describe the hyperbolic operator, thus we do not consider relaxation terms.
The acoustic part of the governing equations is treated implicitly to avoid the
severe restriction on the time step imposed by the CFL condition at low-Mach.
Particular care is taken to discretize the non-conservative terms to avoid
spurious oscillations across multi-material interfaces. The absence of
oscillations and the agreement with analytical or published solutions is
demonstrated in simplified test cases, which confirm the validity of the
proposed approach as a building block on which developing more accurate and
comprehensive methods.
