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

Jan Giesselmann; Charalambos Makridakis; Tristan Pryer

doi:10.1090/S0025-5718-2014-02792-0

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

Jan Giesselmann
, Charalambos Makridakis
, Tristan Pryer

Department of Mathematical Sciences

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

33 Citations (SciVal)

99 Downloads (Pure)

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 language	English
Pages (from-to)	2071-2099
Number of pages	29
Journal	Mathematics of Computation
Volume	83
Early online date	8 Jan 2014
DOIs	https://doi.org/10.1090/S0025-5718-2014-02792-0
Publication status	Published - 2014

Bibliographical note

30 pages, 6 figures, 3 tables

Keywords

math.NA
65M60, 76T10

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10.1090/S0025-5718-2014-02792-0

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

Tristan Pryer
- tmp38bath.acuk
- Institute for Mathematical Innovation (IMI) - Director of the Bath Institute for Mathematical Innovation
- Centre for Therapeutic Innovation
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- IAAPS
- Department of Mathematical Sciences - Professor
Person: Research & Teaching, Core staff, Affiliate staff, Teaching & Other

Cite this

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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. ",

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AU - Giesselmann, Jan

AU - Makridakis, Charalambos

AU - Pryer, Tristan

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PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - math.NA

KW - 65M60, 76T10

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DO - 10.1090/S0025-5718-2014-02792-0

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SN - 1088-6842

VL - 83

SP - 2071

EP - 2099

JO - Mathematics of Computation

JF - Mathematics of Computation

ER -

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

Abstract

Bibliographical note

Keywords

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Tristan Pryer

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