A regularised one-dimensional drop formation and coalescence model using a total variation diminishing (TVD) scheme on a single Eulerian grid

Theo Driessen, Roger Jeurissen

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24 Citations (Scopus)

Abstract

The breakup of an axisymmetric viscous jet is considered in the lubrication approximation. The discretised equations are solved on a fixed equidistant one-dimensional Eulerian grid. The governing equations are implemented in a conservative second order accurate total variation diminishing (TVD) scheme, preventing the numerical diffusivity. Singularities that occur at pinchoff and coalescence are regularised by a small modification on the surface tension. The modification is of the order of the spatial step Dx. This regularisation ensures that the solution of the presented numerical model converges to the exact solution of the breakup of a jet in the lubrication approximation. The results of the presented numerical model agree quantitatively with the analytical solution of the Rayleigh-Plateau instability, and with experimental results on the final stage of the Rayleigh-Plateau instability.

Original languageEnglish
Pages (from-to)333-343
Number of pages11
JournalInternational Journal of Computational Fluid Dynamics
Volume25
Issue number6
DOIs
Publication statusPublished - 1 Jul 2011

Funding

The authors would like to thank Detlef Lohse, Jacco Snoeijer, Arjan van der Bos, Wim de Zeeuw, Herman Wijshoff, Hans Reinten and Marc van den Berg for the valuable discussions on the features of drop formation and the modelling thereof. In addition, the authors would like to thank Federico Toschi for hosting this research. This work has been co-financed by the Dutch ministry of economical affairs, Limburg Province, Overijssel Province, Noord-Brabant Province, the partnership region Eindhoven and by Océ Technologies NV.

Keywords

  • Coalescence
  • Drop formation
  • Free surface flow
  • Lubrication approximation
  • Pinchoff
  • Regularisation of singularities
  • Tvd scheme

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