Research Article

Quantitative benchmark computations of two-dimensional bubble dynamics

  1. S. Hysing1,*,
  2. S. Turek2,
  3. D. Kuzmin2,
  4. N. Parolini3,
  5. E. Burman4,
  6. S. Ganesan5,
  7. L. Tobiska6

Article first published online: 17 NOV 2008

DOI: 10.1002/fld.1934

Issue

International Journal for Numerical Methods in Fluids

International Journal for Numerical Methods in Fluids

Volume 60, Issue 11, pages 1259–1288, 20 August 2009

Additional Information

How to Cite

Hysing, S., Turek, S., Kuzmin, D., Parolini, N., Burman, E., Ganesan, S. and Tobiska, L. (2009), Quantitative benchmark computations of two-dimensional bubble dynamics. Int. J. Numer. Meth. Fluids, 60: 1259–1288. doi: 10.1002/fld.1934

Author Information

  1. 1

    Universitat Politècnica de Catalunya (UPC), Jordi Girona 1-3, Edifici C1, 08034 Barcelona, Spain

  2. 2

    Institut für Angewandte Mathematik, TU Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany

  3. 3

    MOX, Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 29, 20133 Milano, Italy

  4. 4

    Department of Mathematics, University of Sussex, Brighton BN1 9RF, U.K.

  5. 5

    Department of Aeronautics, Imperial College, London, U.K.

  6. 6

    Institut für Analysis und Numerik, Otto-von-Guericke Universität, 39016 Magdeburg, Germany

*Universitat Politècnica de Catalunya (UPC), Jordi Girona 1-3, Edifici C1, 08034 Barcelona, Spain

Publication History

  1. Issue published online: 2 JUL 2009
  2. Article first published online: 17 NOV 2008
  3. Manuscript Accepted: 21 AUG 2008
  4. Manuscript Revised: 15 JUL 2008
  5. Manuscript Received: 12 FEB 2008

Funded by

  • German Research foundation (DFG). Grant Number: To143/9
  • Paketantrag PAK178. Grant Numbers: Tu102/27-1, Ku1530/5-1
  • Sonderforschungsbereich SFB708. Grant Number: TP B7
  • SFB TR R30. Grant Number: TPC3
  • Swiss National Science Foundation. Grant Number: 112166

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Keywords:

  • benchmarking;
  • multiphase flow;
  • rising bubble;
  • numerical simulation;
  • finite-element method;
  • level set method;
  • ALE

Abstract

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 up to the point of break up, 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 up 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 © 2008 John Wiley & Sons, Ltd.

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