Energy consistent DG methods for the Navier Stokes Korteweg system

Giesselmann, Jan and Makridakis, Charalambos and Pryer, Tristan (2012) Energy consistent DG methods for the Navier Stokes Korteweg system. (In Press)

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Abstract

We design consistent discontinuous Galerkin finite element schemes for the approximation of the Euler Korteweg and the Navier Stokes Korteweg systems. We show that the scheme for the Euler Korteweg system is energy and mass conservative and that the scheme for the Navier Stokes Korteweg system is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to viscous efects, that is, there is no numerical dissipation. In this sense the methods is consistent with the energy dissipation of the continuous PDE systems.

Item Type: Article
Subjects: Q Science > QA Mathematics
Depositing User: Dr Jan Giesselmann
Date Deposited: 17 May 2013 06:03
Last Modified: 05 May 2017 13:48
URI: http://preprints.acmac.uoc.gr/id/eprint/228

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