Energy consistent DG methods for the Navier-Stokes-Korteweg system
Numerical Analysis
2014-11-13 v1
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.
Cite
@article{arxiv.1207.4647,
title = {Energy consistent DG methods for the Navier-Stokes-Korteweg system},
author = {Jan Giesselmann and Charalambos Makridakis and Tristan Pryer},
journal= {arXiv preprint arXiv:1207.4647},
year = {2014}
}
Comments
30 pages, 6 figures, 3 tables