Geodesic
Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model
Giesselmann, Jan1 ; Pryer, Tristan2
1 University of Stuttgart, Institute for Applied Analysis and Numerical Simulation, Pfaffenwaldring 57, 70569 Stuttgart, Germany
2 Tristan Pryer, Department of Mathematics and Statistics, Whiteknights, PO Box 220, Reading RG6 6AX, UK
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 1, pp. 275-301

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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.

Reçu le :
DOI : 10.1051/m2an/2014033
Classification : 65M12, 65M60, 76T99, 76D45
Keywords: Quasi-incompressibility, Allen–Cahn, Cahn–Hilliard, Navier–Stokes–Korteweg, phase transition, energy consistent/mimetic, discontinuous Galerkin finite element method

Giesselmann, Jan 1 ; Pryer, Tristan 2

1 University of Stuttgart, Institute for Applied Analysis and Numerical Simulation, Pfaffenwaldring 57, 70569 Stuttgart, Germany
2 Tristan Pryer, Department of Mathematics and Statistics, Whiteknights, PO Box 220, Reading RG6 6AX, UK 
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     title = {Energy consistent discontinuous {Galerkin} methods for a quasi-incompressible diffuse two phase flow model},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {275--301},
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Giesselmann, Jan; Pryer, Tristan. Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 1, pp. 275-301. doi: 10.1051/m2an/2014033

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