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.
DOI : 10.1051/m2an/2014033
Mots clés : Quasi-incompressibility, Allen–Cahn, Cahn–Hilliard, Navier–Stokes–Korteweg, phase transition, energy consistent/mimetic, discontinuous Galerkin finite element method
@article{M2AN_2015__49_1_275_0,
author = {Giesselmann, Jan and Pryer, Tristan},
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},
publisher = {EDP-Sciences},
volume = {49},
number = {1},
year = {2015},
doi = {10.1051/m2an/2014033},
zbl = {1310.76092},
mrnumber = {3342201},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2014033/}
}
TY - JOUR AU - Giesselmann, Jan AU - Pryer, Tristan TI - Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 275 EP - 301 VL - 49 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014033/ DO - 10.1051/m2an/2014033 LA - en ID - M2AN_2015__49_1_275_0 ER -
%0 Journal Article %A Giesselmann, Jan %A Pryer, Tristan %T Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 275-301 %V 49 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014033/ %R 10.1051/m2an/2014033 %G en %F M2AN_2015__49_1_275_0
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. http://www.numdam.org/articles/10.1051/m2an/2014033/
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