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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

Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T -coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients (2013)], we propose a new variational formulation of the…

Numerical Analysis · Mathematics 2024-10-21 Patrick Ciarlet , Erell Jamelot

In this paper, we study an optimal boundary control problem for the Boussinesq equations, which couple the time-dependent Navier-Stokes system with a heat equation, where the control enters through a Robin boundary condition on temperature.…

Numerical Analysis · Mathematics 2026-03-03 Wei Gong , Dongdong Liang , Xianbing Luo , Changlun Ye

This work extends the hydro-mechanical phase-field fracture model to non-isothermal conditions with micromechanics based poroelasticity, which degrades Biot's coefficient not only with the phase-field variable (damage) but also with the…

Numerical Analysis · Mathematics 2024-04-25 Yuhao Liu , Keita Yoshioka , Tao You , Hanzhang Li , Fengshou Zhang

In this work we develop a fictitious domain method for the Stokes problem which allows computations in domains whose boundaries do not depend on the mesh. The method is based on the ideas of Xfem and has been first introduced for the…

Numerical Analysis · Mathematics 2014-01-06 Sébastien Court , Michel Fournié , Alexei Lozinski

This paper proposes and analyzes a full discretization of the exterior transient Stokes problem with Dirichlet boundary conditions. The method is based on a single layer boundary integral representation, using Galerkin semidiscretization in…

Numerical Analysis · Mathematics 2014-10-14 Constantin Bacuta , Matthew E. Hassell , George C. Hsiao , Francisco-Javier Sayas

We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…

Statistical Mechanics · Physics 2015-06-25 Guido Manzi , Rossana Marra

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

In many occurrences of fluid-structure interaction time-periodic motions are observed. We consider the interaction between a fluid driven by the three dimensional Navier-Stokes equation and a two dimensional linearized elastic Koiter shell…

Analysis of PDEs · Mathematics 2024-01-31 Claudiu Mîndrilă , Sebastian Schwarzacher

This work is devoted to the study of the limiting behaviour of the Stokes type fluid flows in porous media. The boundary conditions here are of the Fourier-Neumann's type on the boundary of the holes. Under the periodic hypothesis on the…

Analysis of PDEs · Mathematics 2024-12-25 Lazarus Signing

We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several…

Numerical Analysis · Mathematics 2016-09-08 Winfried Auzinger , Othmar Koch , Michael Quell

The electroporoelasticity model, which couples Maxwell's equations with Biot's equations, plays a critical role in applications such as water conservancy exploration, earthquake early warning, and various other fields. This work focuses on…

Numerical Analysis · Mathematics 2025-02-25 Xuan Liu , Yongkui Zou , Ran Zhang , Yanzhao Cao , Amnon J. Meir

In this paper, we investigate numerically a diffuse interface model for the Navier-Stokes equation with fluid-fluid interface when the fluids have different densities \cite{Lowengrub1998}. Under minor reformulation of the system, we show…

Mathematical Physics · Physics 2015-06-18 Zhenlin Guo , Ping Lin , John S. Lowengrub

Detailed understanding of the coupling between fluid flow and solid deformation in porous media is crucial for the development biomedical devices and novel energy technologies relating to a wide range of geological and biological processes.…

Fluid Dynamics · Physics 2021-09-22 Francisco J. Carrillo

A highly accurate method for simulating surfactant-covered droplets in two-dimensional Stokes flow with solid boundaries is presented. The method handles both periodic channel flows of arbitrary shape and stationary solid constrictions. A…

Numerical Analysis · Mathematics 2020-12-02 Sara Pålsson , Anna-Karin Tornberg

We study several iterative methods for fully coupled flow and reactive transport in porous media. The resulting mathematical model is a coupled, nonlinear evolution system. The flow model component builds on the Richards equation, modified…

Numerical Analysis · Mathematics 2021-01-01 Davide Illiano , Jakub Wiktor Both , Iuliu Sorin Pop , Florin Adrian Radu

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

This paper explores the application of the multiscale finite element method (MsFEM) to address steady-state Stokes-Darcy problems with BJS interface conditions in highly heterogeneous porous media. We assume the existence of multiscale…

Numerical Analysis · Mathematics 2024-01-09 Yachen Hong , Wenhan Zhang , Lina Zhao , Haibiao Zheng

Biot's consolidation model in poroelasticity has a number of applications in science, medicine, and engineering. The model depends on various parameters, and in practical applications these parameters ranges over several orders of…

Numerical Analysis · Mathematics 2016-06-22 Jeonghun J. Lee , Kent-Andre Mardal , Ragnar Winther

In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in [50] is a…

Numerical Analysis · Mathematics 2015-06-03 Jasper Kreeft , Marc Gerritsma