Benchmark configurations for quantitative validation and comparison of
incompressible interfacial flow codes, which model two-dimensional
bubbles rising in liquid columns, are proposed. The benchmark
quantities: circularity, center of mass, and mean rise velocity are
defined and measured to monitor convergence towards a reference
solution. Initial studies are undertaken by three independent research
groups, two representing Eulerian level set finite element codes, and
one representing an ALE moving grid approach.

The first benchmark test case considers a bubble with small density
and viscosity ratios which undergoes moderate shape deformation. The
results from all codes agree very well allowing for target reference
values to be established. For the second test case, a bubble with a
very low density compared to that of the surrounding fluid, the
results for all groups are in good agreement up to the point of break
up, after which all three codes predict different bubble shapes.

All benchmark definitions and results are accessible via the FeatFlow
benchmark repository: http://www.featflow.de/indexcfdbenchmark.html,
where other groups are encouraged to download the presented data or
participate by submitting their own results.