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.
@article{arxiv.2012.01949,
title = {Port-Hamiltonian formulations of poroelastic network models},
author = {Robert Altmann and Volker Mehrmann and Benjamin Unger},
journal= {arXiv preprint arXiv:2012.01949},
year = {2021}
}