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arXiv · 2012.01949

Port-Hamiltonian formulations of poroelastic network models

Robert Altmann·Volker Mehrmann·Benjamin Unger
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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.

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Robert Altmann, Volker Mehrmann, Benjamin Unger. 2020-12-03. Port-Hamiltonian formulations of poroelastic network models. https://arxiv.org/abs/2012.01949

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