Energy consistent DG methods for the Navier-Stokes-Korteweg system

Giesselmann, Jan, Makridakis, Charalambos and Pryer, Tristan (2014) Energy consistent DG methods for the Navier-Stokes-Korteweg system. Mathematics of Computation, 83 (289). pp. 2071-2099. ISSN 0025-5718

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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 effects, 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
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Depositing User: Richard Chambers
Date Deposited: 24 Jan 2018 14:49
Last Modified: 24 Jan 2018 14:49
URI: http://sro.sussex.ac.uk/id/eprint/73117

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