Port-Hamiltonian formulations of poroelastic network models

Authors

R. Altmann, V. Mehrmann, B. Unger

Abstract

We investigate an energy-based formulation of the two-field poroelasticity model and the related multiple-network model as they appear in geosciences or medical applications. We propose a port-Hamiltonian formulation of the system equations, which is beneficial for preserving important system properties after discretization or model-order reduction. For this, we include the commonly omitted second-order term and consider the corresponding first-order formulation. The port-Hamiltonian formulation of the quasi-static case is then obtained by (formally) setting the second-order term zero. Further, we interpret the poroelastic equations as an interconnection of a network of submodels with internal energies, adding a control-theoretic understanding of the poroelastic equations.

Citation

• Journal: Mathematical and Computer Modelling of Dynamical Systems
• Year: 2021
• Volume: 27
• Issue: 1
• Pages: 429–452
• Publisher: Informa UK Limited
• DOI: 10.1080/13873954.2021.1975137

BibTeX

@article{Altmann_2021,
  title={{Port-Hamiltonian formulations of poroelastic network models}},
  volume={27},
  ISSN={1744-5051},
  DOI={10.1080/13873954.2021.1975137},
  number={1},
  journal={Mathematical and Computer Modelling of Dynamical Systems},
  publisher={Informa UK Limited},
  author={Altmann, R. and Mehrmann, V. and Unger, B.},
  year={2021},
  pages={429--452}
}

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