  In 1991, Ramshaw and Mesina proposed a novel synthesis of penalty methods and
artificial compression methods. When the two were balanced they found the
combination was 3-4 orders more accurate than either alone. This report begins
the study of their interesting method applied to the Navier-Stokes equations.
We perform stability analysis, semi-discrete error analysis, and tests of the
algorithm. Although most of the results for implicit time discretizations of
our numerical tests comply with theirs for explicit time discretizations, the
behavior in damping pressure oscillations and violations of incompressibility
are different from their findings and our heuristic analysis.
