Port-Hamiltonian formulations of poroelastic network models

TL;DR

This paper develops a port-Hamiltonian energy-based formulation for poroelastic network models, enhancing the preservation of system properties during discretization and offering a control-theoretic perspective.

Contribution

It introduces a novel port-Hamiltonian formulation for two-field poroelasticity models, including the often omitted second-order term, and interprets the equations as interconnected networks.

Findings

Port-Hamiltonian formulation preserves system properties after discretization.

Inclusion of the second-order term improves model accuracy.

Provides a control-theoretic interpretation of poroelastic equations.

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.