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

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.

33 pages, 8 figures (60 subfigures), 3 tables

References in corpus (2)

• DOLFIN: Automated Finite Element Computing
• Energy consistent DG methods for the Navier-Stokes-Korteweg system

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• A simple, fully-discrete, unconditionally energy-stable method for the two-phase Navier-Stokes Cahn-Hilliard model with arbitrary density ratios
• A structure-preserving numerical method for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems