Incompressible Navier-Stokes Equation as port-Hamiltonian systems: velocity formulation versus vorticity formulation

Authors

Ghislain Haine, Denis Matignon

Abstract

Starting from the description of the isentropic compressible viscous fluid as port-Hamiltonian system in [Mora & al., 2020], the special cases of irrotational or incompressible cases in 2D or 3D are investigated. For the incompressible fluid, the non-linear Navier-Stokes equations are first presented with velocity as energy variable, then analyzed as a modulated port-Hamiltonian system with the help of the vorticity as energy variable. Finally, the structure-preserving numerical scheme provided by the Partitioned Finite Element Method (PFEM) of [Serhani & al., 2019] is applied to the incompressible dissipative fluid in 2D.

Keywords

Navier-Stokes Equations (NSE); Port-Hamiltonian systems (pHs); Incompressible fluid; vorticity; Partitioned Finite Element Method (PFEM)

Citation

• Journal: IFAC-PapersOnLine
• Year: 2021
• Volume: 54
• Issue: 19
• Pages: 161–166
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2021.11.072
• Note: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021- Berlin, Germany, 11-13 October 2021

BibTeX

@article{Haine_2021,
  title={{Incompressible Navier-Stokes Equation as port-Hamiltonian systems: velocity formulation versus vorticity formulation}},
  volume={54},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2021.11.072},
  number={19},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Haine, Ghislain and Matignon, Denis},
  year={2021},
  pages={161--166}
}

Download the bib file

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