  Accurate transport algorithms are crucial for computational fluid dynamics
and more accurate and efficient schemes are always in development. One
dimensional limiting is commonly employed to suppress nonphysical oscillations.
However, the application of such limiters can reduce accuracy. It is important
to identify the weakest set of sufficient conditions required on the limiter as
to allow the development of successful numerical algorithms.
  The main goal of this paper is to identify new less restrictive sufficient
conditions for flux form in-compressible advection to remain monotonic. We
identify additional necessary conditions for incompressible flux form advection
to be monotonic, demonstrating that the Spekreijse limiter region is not
sufficient for incompressible flux form advection to remain monotonic. Then a
convex combination argument is used to derive new sufficient conditions that
are less restrictive than the Sweby region for a discrete maximum principle.
This allows the introduction of two new more general limiter regions suitable
for flux form incompressible advection.
