  Binary star systems are of particular interest to astronomers because they
can be used as astrophysical laboratories to study the properties and processes
of stars. Between 70% to 90% of the stars in our galaxy are part of a binary
star system. Among the many types of binary systems observed, the dynamics of
semi-detached and contact systems are the most interesting because they exhibit
mass transfer, which changes the composition and life cycle of both stars. The
time scales of the mass transfer process are extremely large which makes the
process impossible to capture through physical observation. Computer
simulations have proved invaluable in refining our understanding of the mass
transfer processes. Here we introduce an intuitive, computationally efficient,
gravity centered model that simulates the filling of the Roche lobe of an
expanding star and its transfer of mass through the first Lagrangian point.
