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We develop and analyze a model for the interaction of a quasi-Newtonian free fluid with a poroelastic medium. The flow in the fluid region is described by the nonlinear Stokes equations and in the poroelastic medium by the nonlinear…

Numerical Analysis · Mathematics 2019-02-05 Ilona Ambartsumyan , Vincent J. Ervin , Truong Nguyen , Ivan Yotov

We consider a loosely coupled algorithm for fluid-structure interaction based on a Robin interface condition for the fluid problem (explicit Robin-Neumann scheme). We study the dependence of the stability of this method on the interface…

Numerical Analysis · Mathematics 2019-05-17 Giacomo Gigante , Christian Vergara

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

In this paper, a parallel domain decomposition method is proposed for solving the fully-mixed Stokes-dual-permeability fluid flow model with Beavers-Joseph (BJ) interface conditions. Three Robin-type boundary conditions and a modified weak…

Numerical Analysis · Mathematics 2022-06-14 Zheng Li , Feng Shi , Yizhong Sun , Haibiao Zheng

The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…

Numerical Analysis · Mathematics 2018-04-16 Lucia Carichino , Giovanna Guidoboni , Marcela Szopos

We consider the dynamics of two-phase fluids, in particular the moving contact line, on a solid substrate. The dynamics are governed by the sharp-interface model consisting of the incompressible Navier-Stokes\slash Stokes equations with the…

Computational Physics · Physics 2020-07-15 Quan Zhao , Weiqing Ren

We develop non-overlapping domain decomposition methods for the Biot system of poroelasticity in a mixed form. The solid deformation is modeled with a mixed three-field formulation with weak stress symmetry. The fluid flow is modeled with a…

Numerical Analysis · Mathematics 2021-08-04 Manu Jayadharan , Eldar Khattatov , Ivan Yotov

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

In this paper, we first propose and analyze a novel mixed-type DG method for the coupled Stokes-Darcy problem on simplicial meshes. The proposed formulation is locally conservative. A mixed-type DG method in conjunction with the…

Numerical Analysis · Mathematics 2021-10-01 Lina Zhao

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 a multiphysics model for the flow of Newtonian fluid coupled with Biot consolidation equations through an interface, and incorporating total pressure as an unknown in the poroelastic region. A new mixed-primal finite element…

Numerical Analysis · Mathematics 2023-06-27 Ricardo Ruiz-Baier , Matteo Taffetani , Hans D. Westermeyer , Ivan Yotov

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 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 a novel solution strategy for the Cahn-Hilliard-Biot model, a three-way coupled system that features the interplay of solid phase separation, fluid dynamics, and elastic deformations in porous media. It is a…

Numerical Analysis · Mathematics 2026-02-02 Cedric Riethmüller , Erlend Storvik

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

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 present a loosely coupled, non-iterative time-splitting scheme based on Robin-Robin coupling conditions. We apply a novel unified analysis for this scheme applied to both a Parabolic/Parabolic coupled system and a Parabolic/Hyperbolic…

Numerical Analysis · Mathematics 2021-10-18 Erik Burman , Rebecca Durst , Miguel Fernández , Johnny Guzmán

We introduce a new regularized interface method for proving existence of weak solutions to nonlinear moving boundary problems with low-regularity interfaces. We study a fluid-poroelastic structure interaction (FPSI) problem coupling the…

Analysis of PDEs · Mathematics 2025-08-26 Jeffrey Kuan , Sunčica Čanić , Boris Muha

In the present paper we propose a coupled multigrid method for generalized Stokes flow problems. Such problems occur as subproblems in implicit time-stepping approaches for time-dependent Stokes problems. The discretized Stokes system is a…

Numerical Analysis · Mathematics 2016-01-08 Stefan Takacs