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

Jan Giesselmann, Charalambos Makridakis, Tristan Pryer

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)2071-2099
Number of pages29
JournalMathematics of Computation
Volume83
Early online date8 Jan 2014
DOIs
Publication statusPublished - 2014

Keywords

  • math.NA
  • 65M60, 76T10

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  • 1207.4647v1.PDF

    First published inMathematics of Computation. Vol. 83 (08/01/2014), published by the American Mathematical Society. © 2014 American Mathematical Society.

    Accepted author manuscript, 1.9 MB

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