  The lattice Boltzmann method, now widely used for a variety of applications,
has also been extended to model multi-phase flows through different
formulations. While already applied to many different configurations in the low
Weber and Reynolds number regimes, applications to higher Weber/Reynolds
numbers or larger density/viscosity ratios are still the topic of active
research. In this study, through a combination of the decoupled phase-field
formulation -- conservative Allen-Cahn equation -- and a cumulants-based
collision operator for a low-Mach pressure-based flow solver, we present an
algorithm that can be used for higher Reynolds/Weber numbers. The algorithm is
validated through a variety of test-cases, starting with the Rayleigh-Taylor
instability both in 2-D and 3-D, followed by the impact of a droplet on a
liquid sheet. In all simulations, the solver is shown to correctly capture the
dynamics of the flow and match reference results very well. As the final
test-case, the solver is used to model droplet splashing on a thin liquid sheet
in 3-D with a density ratio of 1000 and kinematic viscosity ratio of 15 --
matching the water/air system -- at We=8000 and Re=1000. The results show that
the solver correctly captures the fingering instabilities at the crown rim and
their subsequent breakup, in agreement with experimental and numerical
observations reported in the literature.
