  A computationally efficient, low order finite element formulation is
developed for modelling the Navier-Stokes-Cahn-Hilliard equations, which have
been established as a promising phase field modelling approach for simulation
of immiscible multiphase flows. The present study suggests that traditional
Navier-Stokes-Cahn-Hilliard models do not allow for surface tension effects to
be neglected due to the presence of the surface tension parameter in the
Cahn-Hilliard equation. This motivates the proposed formulation, which allows
surface tension effects to be changed without affecting the behaviour of the
phase transport. Two methods are proposed: The first uses stabilised SUPG/PSPG
linear elements, while the second is based on mixed Taylor-Hood elements. The
proposed models are applied to a number of benchmark and example problems,
including both capillary regime in which surface tension effects are dominant,
and inertial regime in which surface tension effects are negligibly small. All
results obtained agree very well with reference solutions.
