Two-dimensional rising bubbles
In the absence of analytical solutions, which are very hard to come by for the considered two-phase flow problem class, validation of the mathematical modeling is best accomplished with numerical benchmarking. Pure numerical benchmarks on the other hand are of limited use if they cannot be employed to make quantitative comparisons, mere visual inspection is rarely, if ever, enough to draw hard conclusions. To illustrate this, consider the bubble shapes shown in the figures below
Numerical simulations of a two-dimensional rising bubble for six different codes with identical problem formulations
These shapes were calculated by six different codes with identical problem formulations and should thus ideally give six identical solutions. Unfortunately this is not the case. The shapes are quite similar but it is not possible to tell which solutions, if any, are really correct. In order to be able to do this one must leave the "picture norm" behind and instead use some more rigid metrics with which convergence can be measured directly.
With this in mind two benchmark configurations have been proposed and rigorous benchmark quantities have been defined to measure direct topological parameters, such as interface deformation, and also indirect ones, such as velocity. The task of the proposed benchmarks is to track the evolution of a single two-dimensional bubble rising in a liquid column. This configuration is simple enough to compute accurately yet allows for very complex topology change, giving the interface capturing techniques of today an adequate challenge.
|||Hysing, S.; Turek, S.; Kuzmin, D.; Parolini, N.; Burman, E.; Ganesan, S.; Tobiska, L.: Quantitative benchmark computations of two-dimensional bubble dynamics, International Journal for Numerical Methods in Fluids, Volume 60 Issue 11, Pages 1259-1288, DOI: 10.1002/fld.1934, 2009, [Webpage]|
|||Hysing, S.; Turek, S.; Kuzmin, D.; Parolini, N.; Burman, E.; Ganesan, S.; Tobiska, L.: Proposal for quantitative benchmark computations of bubble dynamics, Ergebnisberichte des Instituts für Angewandte Mathematik, Nummer 351, Fakultät für Mathematik, TU Dortmund, 2007 [PDF]|
|||Hysing, S.; Turek, S.: Benchmark proposals for incompressible two-phase flows, 80, ICMF 2007 Programme and Abstracts of the 6th International Conference on Multiphase Flow, Wiley-VCH, 2007|