We investigate an energy-based formulation of the two-field poroelasticity model and the related multiple-network model as they appear in the 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 taking the formal limit. 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.
%0 Journal Article
%1 AltMU20c
%A Altmann, Robert
%A Mehrmann, Volker
%A Unger, Benjamin
%D 2020
%J ArXiv e-print 2012.01949
%K tag-placeholder
%T Port-Hamiltonian formulations of poroelastic network models
%U https://arxiv.org/abs/2012.01949
%X We investigate an energy-based formulation of the two-field poroelasticity model and the related multiple-network model as they appear in the 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 taking the formal limit. 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{AltMU20c,
abstract = {We investigate an energy-based formulation of the two-field poroelasticity model and the related multiple-network model as they appear in the 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 taking the formal limit. 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.},
added-at = {2021-12-08T17:10:40.000+0100},
author = {{Altmann}, Robert and {Mehrmann}, Volker and {Unger}, Benjamin},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/27750e2cb3f46e772e7005d27373abd77/simtech},
interhash = {0f7476c700d29335b364de9825724611},
intrahash = {7750e2cb3f46e772e7005d27373abd77},
journal = {ArXiv e-print 2012.01949},
keywords = {tag-placeholder},
month = {12},
pubdate = {2020-12-04},
timestamp = {2023-07-31T05:41:23.000+0200},
title = {Port-Hamiltonian formulations of poroelastic network models},
url = {https://arxiv.org/abs/2012.01949},
year = 2020
}
