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Port-Hamiltonian formulations of poroelastic network models

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  • 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.

Suggested Citation

  • R. Altmann & V. Mehrmann & B. Unger, 2021. "Port-Hamiltonian formulations of poroelastic network models," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 27(1), pages 429-452, January.
    • Handle: RePEc:taf:nmcmxx:v:27:y:2021:i:1:p:429-452
    DOI: 10.1080/13873954.2021.1975137
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