Quantitative benchmark computations of two-dimensional 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 toward a reference solution. Comprehensive studies are undertaken by three independent research groups, two representing Eulerian level set finite-element codes and one representing an arbitrary Lagrangian-Eulerian 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 Lip to the point of break Lip, after which all three codes predict different bubble shapes. This highlights the need for the research community to invest more effort in obtaining reference solutions to problems involving break LIP and coalescence. Other research groups are encouraged to participate in these benchmarks by contacting the authors and submitting their own data. The reference data for the computed benchmark quantities can also be Supplied for validation purposes. Copyright (C) 2008 John Wiley & Sons, Ltd.