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The mechanical behaviour of a poroelastic medium permeated by multiple interacting fluid networks can be described by a system of time-dependent partial differential equations known as the multiple-network poroelasticity (MPET) equations or…

Numerical Analysis · Mathematics 2020-10-20 Eleonora Piersanti , Jeonghun J. Lee , Travis Thompson , Kent-Andre Mardal , Marie E. Rognes

In this paper, we present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. The MPET equations describe flow and deformation in an elastic porous medium…

Numerical Analysis · Mathematics 2018-04-23 Jeonghun J. Lee , Eleonora Piersanti , Kent-Andre Mardal , Marie E. Rognes

In this work, we present a new stabilization method aimed at removing spurious oscillations in the pressure approximation of Biot's model for poroelasticity with low permeabilities and/or small time steps. We consider different…

Numerical Analysis · Mathematics 2024-07-30 Álvaro Pé de la Riva , Francisco J. Gaspar , Xiaozhe Hu , James Adler , Carmen Rodrigo , Ludmil Zikatanov

The classical Biot's theory provides the foundation of a fully dynamic poroelasticity model describing the propagation of elastic waves in fluid-saturated media. Multiple network poroelastic theory (MPET) takes into account that the elastic…

Numerical Analysis · Mathematics 2020-04-29 Fadi Philo

This paper presents a novel parallel splitting algorithm for solving quasi-static multiple-network poroelasticity (MPET) equations. By introducing a total pressure variable, the MPET system can be reformulated into a coupled…

Numerical Analysis · Mathematics 2025-07-29 Jijing Zhao , Huangxin Chen , Mingchao Cai , Shuyu Sun

In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well-known…

Numerical Analysis · Mathematics 2021-05-24 Erlend Storvik , Jakub Wiktor Both , Kundan Kumar , Jan Martin Nordbotten , Florin Adrian Radu

The quasi-static multiple network poroelastic theory (MPET) model, first introduced in the context of geomechanics, has recently found new applications in medicine. In practice, the parameters in the MPET equations can vary over several…

Numerical Analysis · Mathematics 2022-05-16 Johannes Kraus , Philip L. Lederer , Maria Lymbery , Kevin Osthues , Joachim Schöberl

We consider unsteady poroelasticity problem in fractured porous medium within the classical Barenblatt double-porosity model. For numerical solution of double-porosity poroelasticity problems we construct splitting schemes with respect to…

Computational Engineering, Finance, and Science · Computer Science 2016-01-26 A. E. Kolesov , P. N. Vabishchevich

We consider a non-linear extension of Biot's model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. We perform an implicit discretization in time (backward Euler) and propose two…

Numerical Analysis · Mathematics 2017-02-02 Manuel Borregales , Florin A. Radu , Kundan Kumar , Jan M. Nordbotten

We consider flux-based multiple-porosity/multiple-permeability poroelasticity systems describing multiple-network flow and deformation in a poro-elastic medium, sometimes also referred to as MPET models. The focus of the paper is on the…

Numerical Analysis · Mathematics 2019-04-01 Qingguo Hong , Johannes Kraus , Maria Lymbery , Mary Fanett Wheeler

The parameters in the governing system of partial differential equations of multicompartmental poroelastic models typically vary over several orders of magnitude making its stable discretization and efficient solution a challenging task. In…

Numerical Analysis · Mathematics 2018-06-12 Qinggou Hong , Johannes Kraus , Maria Lymbery , Fadi Philo

We address numerical solvers for a poromechanics model particularly adapted for soft materials, as it generally respects thermodynamics principles and energy balance. Considering the multi-physics nature of the problem, which involves solid…

Numerical Analysis · Mathematics 2020-11-30 Jakub W. Both , Nicolas A. Barnafi , Florin A. Radu , Paolo Zunino , Alfio Quarteroni

In this paper, we propose a multirate iterative scheme with multiphysics finite element method for a fluid-saturated poroelasticity model. Firstly, we reformulate the original model into a fluid coupled problem to apply the multiphysics…

Numerical Analysis · Mathematics 2021-09-28 Zhihao Ge , Xiangzi Fu

In this paper, we develop the numerical theory of decoupled modified characteristic finite element method with different subdomain time steps for the mixed stabilized formulation of nonstationary dual-porosity-Navier-Stokes model. Based on…

Numerical Analysis · Mathematics 2020-08-19 Luling Cao , Yinnian He , Jian Li

In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…

Numerical Analysis · Computer Science 2013-11-18 A. E. Kolesov , P. N. Vabishchevich , M. V. Vasilyeva

This paper introduces a unified model for thermo-poroelasticity and multiple-network poroelasticity, reformulated into a total-pressure-based system. We first establish the well-posedness of the problem via a Galerkin-based argument and…

Numerical Analysis · Mathematics 2026-04-01 Huipeng Gu , Mingchao Cai , Jingzhi Li , Yu Jiang

We consider a poromechanics model including frictionless contact mechanics. The resulting model consists of the Biot equations with contact boundary conditions leading to a variational inequality modelling mechanical deformations coupled to…

Numerical Analysis · Mathematics 2024-07-19 Tameem Almani , Kundan Kumar

An alternative to the fully implicit or monolithic methods used for the solution of the coupling of fluid flow and deformation in porous media is a sequential approach in which the fully coupled system is broken into subproblems (flow and…

Numerical Analysis · Mathematics 2025-12-23 Xiaozhe Hu , Francisco J. Gaspar , Carmen Rodrigo

In this work, we study the parallel-in-time iterative solution of coupled flow and geomechanics in porous media, modelled by a two-field formulation of the Biot's equations. In particular, we propose a new version of the fixed stress…

Numerical Analysis · Mathematics 2018-02-06 Manuel Borregales , Kundan Kumar , Florin Adrian Radu , Carmen Rodrigo , Francisco José Gaspar

We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types…

Numerical Analysis · Mathematics 2023-07-19 Carmen Rodrigo , Francisco Gaspar , Xiaozhe Hu , Ludmil Zikatanov
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