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In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such nonlinear models are…

Numerical Analysis · Mathematics 2024-01-01 Johannes Kraus , Kundan Kumar , Maria Lymbery , Florin Adrian Radu

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

This work serves as a primer to our efforts in arriving at convergence estimates for the fixed stress split iterative scheme for single phase flow coupled with small strain anisotropic poroelastoplasticity. The fixed stress split iterative…

Numerical Analysis · Mathematics 2018-10-11 Saumik Dana , Mary F. Wheeler

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

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 fixed-stress splitting scheme is a popular method for iteratively solving the Biot equations. The method successively solves the flow and mechanic subproblems while adding a stabilizing term to the flow equation, which includes a…

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

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the…

Numerical Analysis · Mathematics 2024-02-19 Ryan M. Aronson , Nicola Castelletto , François P. Hamon , J. A. White , Hamdi A. Tchelepi

In this work, we present numerical studies of fixed-stress iterative coupling for solving flow and geomechanics with propagating fractures in a porous medium. Specifically, fracture propagations are described by employing a phase-field…

Numerical Analysis · Mathematics 2017-09-07 Sanghyun Lee , Thomas Wick , Mary F. Wheeler

In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model. To better describe the processes of deformation and diffusion, we firstly reformulate the nonlinear fluid-solid coupling problem into a…

Numerical Analysis · Mathematics 2021-12-28 Zhihao Ge , Wenlong He

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

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

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

We arrive at convergence criterion for the fixed stress split iterative scheme for single phase flow coupled with small strain anisotropic poroelastoplasticity. The analysis is based on studying the equations satisfied by the difference of…

Numerical Analysis · Mathematics 2021-07-29 Saumik Dana , Mary F Wheeler

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

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

Within this paper, we introduce and analyze a novel time stepping scheme for linear poroelasticity. In each time frame, we iteratively solve the flow and mechanics equations with an additional damping step for the pressure variable.…

Numerical Analysis · Mathematics 2025-03-12 R. Altmann , M. Deiml

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

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 work we analyze an optimized artificial fixed-stress iteration scheme for the numerical approximation of the Biot system modelling fluid flow in deformable porous media. The iteration is based on a prescribed constant artificial…

Numerical Analysis · Mathematics 2017-05-24 M. Bause , F. A. Radu , U. Köcher

We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…

Numerical Analysis · Mathematics 2026-04-28 Andrea Bonito , Vivette Girault , Diane Guignard
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