A Scalable port-Hamiltonian Model for Incompressible Fluids in Irregular Geometries

Authors

Luis A. Mora, Héctor Ramírez, Juan I. Yuz, Yann Le Gorrec

Abstract

The behavior of a fluid in pipes with irregular geometries is studied. Departing from the partial differential equations that describe mass and momentum balances a scalable lumped-parameter model is proposed. To this end the framework of port-Hamiltonian systems is instrumental to derive a modular system which upon interconnection describes segments with different cross sections and dissipation effects. In order to perform the interconnection between different segments the incompressibility hypothesis is relaxed in some infinitesimal section to admit density variations and energy transference between segments. Numerical simulations are performed in order to illustrate the model.

Keywords

Port-Hamiltonian systems; PDE; approximation of PDEs; computational methods

Citation

• Journal: IFAC-PapersOnLine
• Year: 2019
• Volume: 52
• Issue: 2
• Pages: 102–107
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2019.08.018
• Note: 3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations CPDE 2019- Oaxaca, Mexico, 20–24 May 2019

BibTeX

@article{Mora_2019,
  title={{A Scalable port-Hamiltonian Model for Incompressible Fluids in Irregular Geometries}},
  volume={52},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2019.08.018},
  number={2},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Mora, Luis A. and Ramírez, Héctor and Yuz, Juan I. and Gorrec, Yann Le},
  year={2019},
  pages={102--107}
}

Download the bib file

References

• Altmann, R. & Schulze, P. A port-Hamiltonian formulation of the Navier–Stokes equations for reactive flows. Systems & Control Letters vol. 100 51–55 (2017) – 10.1016/j.sysconle.2016.12.005
• Bird, (2014)
• Bourantas, G. C., Cheeseman, B. L., Ramaswamy, R. & Sbalzarini, I. F. Using DC PSE operator discretization in Eulerian meshless collocation methods improves their robustness in complex geometries. Computers & Fluids vol. 136 285–300 (2016) – 10.1016/j.compfluid.2016.06.010
• Brodkey, Transport Phenomena: A Unified Approach. (2003)
• Cal, I. R., Cercos-Pita, J. L. & Duque, D. The incompressibility assumption in computational simulations of nasal airflow. Computer Methods in Biomechanics and Biomedical Engineering vol. 20 853–868 (2017) – 10.1080/10255842.2017.1307343
• Duindam, (2009)
• Guidoboni, G., Glowinski, R., Cavallini, N., Canic, S. & Lapin, S. A kinematically coupled time-splitting scheme for fluid–structure interaction in blood flow. Applied Mathematics Letters vol. 22 684–688 (2009) – 10.1016/j.aml.2008.05.006
• Hager, Losses in Flow. (2010)
• Johnson, (2016)
• Kotyczka, P. & Maschke, B. Discrete port-Hamiltonian formulation and numerical approximation for systems of two conservation laws. at - Automatisierungstechnik vol. 65 308–322 (2017) – 10.1515/auto-2016-0098
• Mulley, (2004)
• Murdock, (1993)
• Pérez-García, J., Sanmiguel-Rojas, E. & Viedma, A. New coefficient to characterize energy losses in compressible flow at T-junctions. Applied Mathematical Modelling vol. 34 4289–4305 (2010) – 10.1016/j.apm.2010.05.005
• Sharatchandra, M. C. & Rhode, D. L. NEW. STRONGLY CONSERVATIVE FINITE-VOLUME FORMULATION FOR FLUID FLOWS IN IRREGULAR GEOMETRIES USING CONTRAVARIANT VELOCITY COMPONENTS: PART 1. THEORY. Numerical Heat Transfer, Part B: Fundamentals vol. 26 39–52 (1994) – 10.1080/10407799408914915
• Trenchant, V., Ramirez, H., Le Gorrec, Y. & Kotyczka, P. Finite differences on staggered grids preserving the port-Hamiltonian structure with application to an acoustic duct. Journal of Computational Physics vol. 373 673–697 (2018) – 10.1016/j.jcp.2018.06.051
• van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics vol. 42 166–194 (2002) – 10.1016/s0393-0440(01)00083-3
• van der Schaft, A. L2-Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer International Publishing, 2017). doi:10.1007/978-3-319-49992-5 – 10.1007/978-3-319-49992-5
• van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
• Wu, Z. & Cao, Y. Numerical simulation of flow over an airfoil in heavy rain via a two-way coupled Eulerian–Lagrangian approach. International Journal of Multiphase Flow vol. 69 81–92 (2015) – 10.1016/j.ijmultiphaseflow.2014.11.006