Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model

Jan Giesselmann, Tristan Pryer

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)
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Abstract

We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen-Cahn/Cahn-Hilliard/Navier-Stokes-Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.
Original languageEnglish
Pages (from-to)275-301
Number of pages27
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume49
Issue number1
Early online date30 Jan 2015
DOIs
Publication statusPublished - 31 Jan 2015

Keywords

  • math.NA
  • 65M12, 65M60, 76T99, 76D45

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