Port-Hamiltonian formulations of poroelastic network models. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Altmann, R.; Mehrmann, V.; Unger, B.
• Is Part Of: Mathematical and computer modelling of dynamical systems. Volume 27:Issue 1(2021)
• Page Start: 429
• Page End: 452
• Publication Date: 2021-01-02
• Subjects: Poroelastic network model -- port-Hamiltonian system -- differential-algebraic operator equation -- dissipative Hamiltonian system; Engineering -- Mathematical models -- Periodicals; Computer simulation -- Periodicals; 515.39
• DOI: 10.1080/13873954.2021.1975137
• Languages: English
• ISSNs: 1387-3954

Abstract

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.