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The paper deals with modelling fluid saturated porous media subject to large deformation. An Eulerian incremental formulation is derived using the problem imposed in the spatial configuration in terms of the equilibrium equation and the…

Numerical Analysis · Mathematics 2018-01-17 Eduard Rohan , Vladimír Lukeš

In this paper, we propose a numerical method for computing solutions to Biot's fully dynamic model of incompressible saturated porous media [Biot;1956]. Our spatial discretization scheme is based on the three-field formulation (u-w-p) and…

Numerical Analysis · Mathematics 2015-06-24 Zahrasadat Lotfian , Mettupalayam Sivaselvan

An explicit finite-difference scheme is presented for solving the two-dimensional Biot equations of poroelasticity across the full range of frequencies. The key difficulty is to discretize the Johnson-Koplik-Dashen (JKD) model which…

Classical Physics · Physics 2013-12-11 Emilie Blanc , Guillaume Chiavassa , Bruno Lombard

We propose the generalisation of the anisotropic poroelasticity theory. At a large scale, a medium is viewed as quasi-static, which is the original assumption of Biot. At a smaller scale, we distinguish different porosity clusters (sets of…

We consider a poroelastic medium with a thin heterogeneity, also referred to as a fracture. Fluid flow and mechanical deformation inside both bulk and fracture are governed by the quasi-static Biot equations. The fracture's material…

Analysis of PDEs · Mathematics 2025-12-05 Maximilian Hörl , Kundan Kumar , Christian Rohde

We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

Analysis of PDEs · Mathematics 2024-08-27 Helmut Abels , Harald Garcke , Jonas Haselböck

In this paper, the analysis and homogenization of a poroelastic model for the hydro-mechanical response of fibre-reinforced hydrogels is considered. Here, the medium in question is considered to be a highly heterogeneous two-component media…

Analysis of PDEs · Mathematics 2023-11-27 Michael Eden , Hari Shankar Mahato

We develop a theory for drying-induced stresses in sessile, poroelastic drops undergoing evaporation on rigid surfaces. Using a lubrication-like approximation, the governing equations of three-dimensional nonlinear poroelasticity are…

Soft Condensed Matter · Physics 2022-05-18 Matthew G. Hennessy , Richard V. Craster , Omar K. Matar

The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin shell is considered, as the thickness $h$ of the shell tends to zero. Given the appropriate scalings of the applied force and of the initial data…

Analysis of PDEs · Mathematics 2018-04-17 Yizhao Qin , Pengfei Yao

We resolve the issue of uniqueness of weak solutions for linear, inertial fluid-poroelastic-structure coupled dynamics. The model comprises a 3D Biot poroelastic system coupled to a 3D incompressible Stokes flow via a 2D interface, where…

Analysis of PDEs · Mathematics 2025-02-12 George Avalos , Justin T. Webster

This paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static poroelastic model (also known as Biot's model). It consists…

Analysis of PDEs · Mathematics 2018-07-05 Mats K. Brun , Elyes Ahmed , Florin A. Radu , Jan Martin Nordbotten

We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is governed by the Stokes equations, while the flow in the…

Numerical Analysis · Mathematics 2017-10-19 Ilona Ambartsumyan , Eldar Khattatov , Ivan Yotov , Paolo Zunino

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

In this paper we consider a family of three-dimensional problems in thermoelasticity for linear elliptic membrane shells and study the asymptotic behaviour of the solution when the thickness tends to zero.We fully characterize with strong…

Analysis of PDEs · Mathematics 2020-12-22 M. T. Cao-Rial , G. Castiñeira , Á. Rodríguez-Arós , S. Roscani

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 quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…

Analysis of PDEs · Mathematics 2022-02-23 Lorena Bociu , Boris Muha , Justin T. Webster

The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress…

Numerical Analysis · Mathematics 2020-01-22 Kundan Kumar , Svetlana Kyas , Jan Nordbotten , Sergey Repin

We consider the dynamic Biot model describing the interaction between fluid flow and solid deformation including wave propagation phenomena in both the liquid and solid phases of a saturated porous medium. The model couples a hyperbolic…

Numerical Analysis · Mathematics 2024-01-10 Johannes Kraus , Maria Lymbery , Kevin Osthues , Fadi Philo

A time-domain numerical modeling of transversely isotropic Biot poroelastic waves is proposed in two dimensions. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by…

Computational Physics · Physics 2015-06-24 Emilie Blanc , Guillaume Chiavassa , Bruno Lombard

In this paper, we consider the numerical approximation of the quasi-static, linear Biot model in a 3D domain $\Omega$ when the right-hand side of the mass balance equation is concentrated on a 1D line source $\delta_{\Lambda}$. This model…

Numerical Analysis · Mathematics 2020-01-07 Nadia S. Taki , Ingeborg G. Gjerde