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

Giesselmann, J. and Pryer, T. (2015) Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model. ESAIM: Mathematical Modelling and Numerical Analysis M2AN, 49 (1). pp. 275-301. ISSN 1290-3841

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To link to this item DOI: 10.1051/m2an/2014033

Abstract/Summary

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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:40918
Publisher:EDP Sciences

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