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Energy consistent DG methods for the Navier-Stokes-Korteweg system
journal contribution
posted on 2023-06-09, 11:45 authored by Jan Giesselmann, Charalambos MakridakisCharalambos Makridakis, Tristan PryerWe 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.
History
Publication status
- Published
File Version
- Accepted version
Journal
Mathematics of ComputationISSN
0025-5718Publisher
American Mathematical SocietyExternal DOI
Issue
289Volume
83Page range
2071-2099Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Numerical Analysis and Scientific Computing Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-01-24First Open Access (FOA) Date
2018-01-24First Compliant Deposit (FCD) Date
2018-01-24Usage metrics
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