WIAS Preprint No. 1823, (2013)

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


  • Giesselmann, Jan
  • Pryer, Tristan

2010 Mathematics Subject Classification

  • 65M12 65M60 76T99 76D45


  • Quasi-incompressibility, Allen--Cahn, Cahn--Hilliard, Navier--Stokes--Korteweg, phase transition, energy consistent/mimetic, discontinuous Galerkin finite element method


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.

Appeared in

  • Mathematical Modeling and Numerical Analysis M2AN, 49(1) (2015), pp. 275--301.

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