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.

摘要

我们研究了双场多孔弹性模型和相关多网络模型在地球科学或医学应用中出现的基于能量的公式。我们提出了系统方程的 port-Hamiltonian 公式，这有利于在离散化或模型降阶后保留重要的系统属性。为此，我们包括通常省略的二阶项并考虑相应的一阶公式。然后通过（正式）将二阶项设置为零来获得准静态情况的哈密尔顿公式。此外，我们将多孔弹性方程解释为具有内能的子模型网络的互连，增加了对多孔弹性方程的控制理论理解。