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Related papers: Robust iterative schemes for non-linear poromechan…

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We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand it…

Numerical Analysis · Mathematics 2023-07-19 Martina Bukac , Ivan Yotov , Rana Zakerzadeh , Paolo Zunino

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

We develop a mixed finite element domain decomposition method on non-matching grids for the Biot system of poroelasticity. A displacement-pressure vector mortar function is introduced on the interfaces and utilized as a Lagrange multiplier…

Numerical Analysis · Mathematics 2024-09-13 Manu Jayadharan , Ivan Yotov

In this work we consider the transport of a surfactant in a variably saturated porous media. The water flow is modelled by the Richards equations and it is fully coupled with the transport equation for the surfactant. Three linearization…

Numerical Analysis · Mathematics 2020-12-23 Davide Illiano , Iuliu Sorin Pop , Florin Adrian Radu

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

We investigate the fluid-poroelastic structure interaction problem in a moving domain, governed by Navier-Stokes-Biot (NSBiot) system. First, we propose a fully parallelizable, loosely coupled scheme to solve the coupled system. At each…

Numerical Analysis · Mathematics 2024-09-25 Shihan Guo , Yizhong Sun , Yifan Wang , Xiaohe Yue , Haibiao Zheng

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

In this paper, we study the robust linearization of nonlinear poromechanics of unsaturated materials. The model of interest couples the Richards equation with linear elasticity equations, employing the equivalent pore pressure. In practice…

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

In this work, we propose a structure-preserving discretisation for the recently studied Cahn-Hilliard-Biot system using conforming finite elements in space and problem-adapted explicit-implicit Euler time integration. We prove that the…

Numerical Analysis · Mathematics 2024-07-18 Aaron Brunk , Marvin Fritz

We introduce a stress/total-pressure formulation for poroelasticity that includes the coupling with steady nonlinear diffusion modified by stress. The nonlinear problem is written in mixed-primal form, coupling a perturbed twofold…

Numerical Analysis · Mathematics 2023-06-27 Bryan Gomez-Vargas , Kent-Andre Mardal , Ricardo Ruiz-Baier , Vegard Vinje

This paper presents a study of solution strategies for the Cahn-Hilliard-Biot equations, a complex mathematical model for understanding flow in deformable porous media with changing solid phases. Solving the Cahn-Hilliard-Biot system poses…

Numerical Analysis · Mathematics 2024-01-25 Erlend Storvik , Cedric Riethmüller , Jakub Wiktor Both , Florin Adrian Radu

A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…

Numerical Analysis · Mathematics 2025-03-03 Herbert Egger , Andreas Schafelner

We develop and analyze a splitting method for fluid-poroelastic structure interaction. The fluid is described using the Stokes equations and the poroelastic structure is described using the Biot equations. The transmission conditions on the…

Numerical Analysis · Mathematics 2024-09-30 Aashi Dalal , Rebecca Durst , Annalisa Quaini , Ivan Yotov

Multilayered poroelastic structures are found in many biological tissues such as cartilage and the cornea, and play a key role in the design of bioartificial organs and other bioengineering applications. Motivated by these applications, we…

Numerical Analysis · Mathematics 2025-07-15 Andrew Scharf , Martina Bukač , Sunčica Čanić

In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic equation. The proposed…

Numerical Analysis · Mathematics 2017-05-02 Florin Adrian Radu , Kundan Kumar , Jan Martin Nordbotten , Iuliu Sorin Pop

Biot's consolidation model is a classical model for the evolution of deformable porous media saturated by a fluid and has various interdisciplinary applications. While numerical solution methods to solve poroelasticity by typical schemes…

Numerical Analysis · Mathematics 2026-05-21 Stephan B. Lunowa , Barbara Wohlmuth

We proposed a parallel-in-time method based on preconditioner for Biot's consolidation model in poroelasticity. In order to achieve a fast and stable convergence for the matrix system of the Biot's model, we design two preconditioners with…

Numerical Analysis · Mathematics 2023-10-17 Zeyuan Zhou , Huipeng Gu , Guoliang Ju , Wei Xing

We introduce a semi-explicit time-stepping scheme of second order for linear poroelasticity satisfying a weak coupling condition. Here, semi-explicit means that the system, which needs to be solved in each step, decouples and hence improves…

Numerical Analysis · Mathematics 2023-11-08 R. Altmann , R. Maier , B. Unger

In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several…

Optimization and Control · Mathematics 2023-06-08 Chenzheng Guo , Jing Zhao

Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…

Computational Engineering, Finance, and Science · Computer Science 2018-01-22 Petr N. Vabishchevich