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Related papers: Fully-Mixed Virtual Element Method for the Biot Pr…

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We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are distinct in bulk and on…

Soft Condensed Matter · Physics 2023-05-16 Jaemin Kim , Ida Ang , Francesco Ballarin , Chung-Yuen Hui , Nikolaos Bouklas

In this paper, we propose a new multiphysics finite element method for a Biot model with secondary consolidation in soil dynamics. To better describe the processes of deformation and diffusion underlying in the original model, we…

Numerical Analysis · Mathematics 2022-04-08 Zhihao Ge , Wenlong He

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

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

The accurate description of fluid flow and transport in fractured porous media is of paramount importance to capture the macroscopic behaviour of an oil reservoir, a geothermal system, or a CO2 sequestration site, to name few applications.…

Numerical Analysis · Mathematics 2019-08-01 Alessio Fumagalli , Eirik Keilegavlen

In this paper, we propose and analyze a mixed formulation for the Kelvin-Voigt-Brinkman-Forchheimer equations for unsteady viscoelastic flows in porous media. Besides the velocity and pressure, our approach introduces the vorticity as a…

Numerical Analysis · Mathematics 2024-06-25 Sergio Caucao , Ivan Yotov

In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in…

Numerical Analysis · Mathematics 2015-08-11 Donald L. Brown , Maria Vasilyeva

Pressure oscillations at small time steps have been known to be an issue in poroelasticity simulations. A review of proposed approaches to overcome this problem is presented. Critical time steps are specified to alleviate this in finite…

Numerical Analysis · Mathematics 2025-02-26 Yared W. Bekele , Eivind Fonn , Trond Kvamsdal , Arne M. Kvarving , Steinar Nordal

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

Poroelasticity theory models the dynamics of porous, fluid-saturated media. It was pioneered by Maurice Biot in the 1930s through 1960s, and has applications in several fields, including geophysics and modeling of in vivo bone. A wide…

Numerical Analysis · Mathematics 2012-11-29 Grady I. Lemoine , M. Yvonne Ou , Randall J. LeVeque

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…

Analysis of PDEs · Mathematics 2022-01-03 Mina Karimi , Mehrdad Massoudi , Noel Walkington , Matteo Pozzi , Kaushik Dayal

We develop a family of mixed finite element methods for a model of nonlinear poroelasticity where, thanks to a rewriting of the constitutive equations, the permeability depends on the total poroelastic stress and on the fluid pressure and…

Numerical Analysis · Mathematics 2025-02-25 Arbaz Khan , Bishnu P. Lamichhane , Ricardo Ruiz-Baier , Segundo Villa-Fuentes

We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…

Numerical Analysis · Mathematics 2022-09-26 Franco Dassi , Alessio Fumagalli , Ilario Mazzieri , Giuseppe Vacca

This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\rm div)$ conforming virtual element method (VEM) for the approximation of the…

Numerical Analysis · Mathematics 2024-05-13 Sarvesh Kumar , Devika Shylaja

We present a priori error analysis for a fully discrete, parallelizable, explicit loosely coupled scheme for the time-dependent Stokes-Biot problem. The method decouples the fluid and poroelastic subproblems in a fully explicit fashion,…

Numerical Analysis · Mathematics 2026-03-24 Yifan Wang , Jeonghun Lee , Suncica Canic

We study the fully mixed formulation of the Biot equations, which is characterized by a symmetric coupling between flow and deformation. This structure enables the use of stable mixed finite elements for each subproblem without a strong…

Numerical Analysis · Mathematics 2026-03-20 Fleurianne Bertrand , Jakub Wiktor Both , Tugay Dağlı

This paper studies the thermo-poroelasticity model. By introducing an intermediate variable, we transform the original three-field model into a four-field model. Building upon this four-field model, we present both a coupled finite element…

Numerical Analysis · Mathematics 2025-07-23 Mingchao Cai , Jingzhi Li , Ziliang Li , Qiang Liu

The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous…

Computational Engineering, Finance, and Science · Computer Science 2018-05-23 S. H. S. Joodat , K. B. Nakshatrala , R. Ballarini

We present projection-based mixed finite element methods for the solution of the unsteady Brinkman equations for incompressible single-phase flow with fixed in space porous solid inclusions. At each time step the method requires the…

Numerical Analysis · Mathematics 2025-09-24 Costanza Aricò , Rainer Helmig , Ivan Yotov

This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The…

Numerical Analysis · Mathematics 2023-12-05 Paola F. Antonietti , Michele Botti , Ilario Mazzieri
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