Proposal for quantitative benchmark computations of bubble dynamics

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: www.featflow.de/indexcfdbenchmark.html, where other groups are encouraged to download the presented data or participate by submitting their own results.