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In this work, we consider fracture propagation in nearly incompressible and (fully) incompressible materials using a phase-field formulation. We use a mixed form of the elasticity equation to overcome volume locking effects and develop a…

Numerical Analysis · Mathematics 2022-02-10 Timo Heister , Katrin Mang , Thomas Wick

A nonlinear model relating the imposed motion of a circular cylinder, submerged in a fluid flow, to the transverse force coefficient is presented. The nonlinear fluid system, featuring vortex shedding patterns, limit cycle oscillations and…

Fluid Dynamics · Physics 2020-06-11 Jan Decuyper , Tim De Troyer , Koen Tiels , Johan Schoukens , Mark C. Runacres

In this paper, we consider the wave propagations of viscoelastic materials, which has been derived by Taiping-Liu to approximate the viscoelastic dynamic system with fading memory (see [T.P.Liu(1988)\cite{LiuTP}]) by the Chapman-Enskog…

Analysis of PDEs · Mathematics 2025-09-12 Zhenhua Guo , Meichen Hou , Guiqin Qiu , Lingda Xu

This paper is devoted to a weak Galerkin (WG) finite element method for linear poroelasticity problems where weakly defined divergence and gradient operators over discontinuous functions are introduced. We establish both the continuous and…

Numerical Analysis · Mathematics 2022-08-10 Shanshan Gu , Shimin Chai , Chenguang Zhou

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 consider the flow of a viscous incompressible fluid through a porous medium. We allow the permeability of the medium to depend exponentially on the pressure and provide an analysis for this model. We study a splitting formulation where a…

Analysis of PDEs · Mathematics 2020-11-06 Zerihun Kinfe Birhanu , Tadele Mengesha , Abner J. Salgado

Poroelasticity is an example of coupled processes which are crucial for many applications including safety assessment of radioactive waste repositories. Numerical solution of poroelasticity problems discretized with finite volume -- virtual…

Numerical Analysis · Mathematics 2022-10-20 Denis Anuprienko

We study the diffusion-reaction-advection model for mobile chemical species together with the dissolution and precipitation of immobile species in a porous medium at the micro-scale. This leads to a system of semilinear parabolic partial…

Analysis of PDEs · Mathematics 2022-09-16 Nibedita Ghosh , Hari Shankar Mahato

We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in…

We propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or…

Applied Physics · Physics 2025-07-22 Ilaria Fontana , Goustan Bacquaert , Daniele A. Di Pietro , Kyrylo Kazymyrenko

We study incompressible fluid flow through a thin poroelastic layer and rigorously derive a macroscopic model when the thickness of the layer tends to zero. Within the layer we assume a periodic structure and both, the periodicity and the…

Analysis of PDEs · Mathematics 2024-03-08 Markus Gahn

In this paper we investigate the limit behavior of the solution to quasi-static Biot's equations in thin poroelastic flexural shells as the thickness of the shell tends to zero and extend the results obtained for the poroelastic plate by…

Analysis of PDEs · Mathematics 2015-04-24 Andro Mikelic , Josip Tambaca

We study nonlinear reactive transport in a layered porous medium separated by an $\varepsilon$-thin, highly heterogeneous fracture whose aperture and obstacle pattern vary periodically. Species transport in the bulk is governed by parabolic…

Analysis of PDEs · Mathematics 2026-02-19 Taras Mel'nyk , Sorin Pop , Christian Rohde

We present an implicit, fully-coupled hydro-mechanical solver for the three dimensional simulation of fluid-driven rupture propagation along existing discontinuities. The solver handles simultaneously frictional slip (shear failure) and…

We study a fluid-poroelasticity interaction (FPSI) problem coupling the unsteady Stokes equations with the fully dynamic Biot system. A major challenge in such problems is to design partitioned schemes that remain robust in locking-related…

Numerical Analysis · Mathematics 2026-04-13 Wenlong He , Thomas Wick , Xiaohe Yue , Jiwei Zhang , Haibiao Zheng

In this paper, the inherent gradient flow structures of thermo-poro-visco-elastic processes in porous media are examined for the first time. In the first part, a modelling framework is introduced aiming for describing such processes as…

Numerical Analysis · Mathematics 2019-11-27 Jakub Wiktor Both , Kundan Kumar , Jan Martin Nordbotten , Florin Adrian Radu

Nonlinear hydrodynamic equations for visco-elastic media are discussed. We start from the recently derived fully hydrodynamic nonlinear description of permanent elasticity that utilizes the (Eulerian) strain tensor. The reversible quadratic…

Soft Condensed Matter · Physics 2007-05-23 Harald Pleiner , Mario Liu , Helmut R. Brand

The motion of flexible fibers through structured fluidic environments is ubiquitous in nature and industrial applications. Most often, their dynamics results from the complex interplay between internal elastic stresses, contact forces and…

Fluid Dynamics · Physics 2022-09-23 Ursy Makanga , Mohammadreza Sepahi , Camille Duprat , Blaise Delmotte

We consider degenerate porous medium equations with a divergence type of drift terms. We establish the existence of $L^{q}$-weak solutions (satisfying energy estimates or even further with moment and speed estimates in Wasserstein spaces),…

Analysis of PDEs · Mathematics 2023-03-07 Sukjung Hwang , Kyungkeun Kang , Haw Kil Kim

A quasi-static filtration system, comprising a poroelastic solid coupled to an incompressible free-flow, is considered in 3D. Across a flat 2D interface, the Beavers-Joseph-Saffman coupling conditions are taken. The system constitutes a…

Analysis of PDEs · Mathematics 2026-05-15 Peter Lavagnino , Arum Lee , Justin T. Webster