  The conservation of mass is common issue with multiphase fluid simulations.
In this work a novel projection method is presented which conserves mass both
locally and globally. The fluid pressure is augmented with a time-varying
component which accounts for any global mass change. The resulting system of
equations is solved using an efficient Schur-complement method. Using the
proposed method four numerical examples are performed: the evolution of a
static bubble, the rise of a bubble, the breakup of a thin fluid thread, and
the extension of a droplet in shear flow. The method is capable of conserving
the mass even in situations with morphological changes such as droplet breakup.
