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Related papers: A Robin-Robin splitting method for the Stokes-Biot…

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We present a new splitting method for time-dependent convection-dominated diffusion problems. The original convection diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a…

Mathematical Physics · Physics 2013-02-19 Feng Shi , Guoping Liang , Yubo Zhao , Jun Zou

We study a mathematical model of fluid -- poroelastic structure interaction and its numerical solution. The free fluid region is governed by the unsteady incompressible Navier-Stokes equations, while the poroelastic region is modeled by the…

Numerical Analysis · Mathematics 2025-03-18 Xing Wang , Ivan Yotov

The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…

Numerical Analysis · Mathematics 2020-03-19 Ondrej Maxian , Charles S. Peskin

This paper investigates the heat equation on a bounded domain with a Robin boundary condition, where the reactivity parameter (or killing rate) is modeled as a continuous-time Markov chain. We analyze the system under two stochastic…

Probability · Mathematics 2026-05-01 Fausto Colantoni

We develop a linearly-scaling variant of the Force Coupling Method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205-231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly-periodic geometry with either a…

Computational Physics · Physics 2023-05-03 Aref Hashemi , Raul P. Pelaez , Sachin Natesh , Brennan Sprinkle , Ondrej Maxian , Zecheng Gan , Aleksandar Donev

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

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

Rigid particles in a Stokesian fluid can physically not overlap, as a thin layer of fluid always separates a particle pair, exerting increasingly strong repulsive forces on the bodies for decreasing separations. Numerically, resolving these…

Fluid Dynamics · Physics 2024-06-11 Anna Broms , Anna-Karin Tornberg

This paper presents a rigorous derivation of an effective model for fluid flow through a thin elastic porous membrane separating two fluid bulk domains. The microscopic setting involves a periodically structured porous membrane composed of…

Analysis of PDEs · Mathematics 2025-08-07 Markus Gahn , Maria Neuss-Radu

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 numerical methods to simulate the fluid-mechanical erosion of many bodies in two-dimensional Stokes flow. The broad aim is to simulate the erosion of a porous medium (e.g. groundwater flow) with grain-scale resolution. Our fluid…

Numerical Analysis · Mathematics 2018-09-26 Bryan D. Quaife , M. Nicholas J. Moore

In this paper, we propose a numerical method for computing solutions to Biot's fully dynamic model of incompressible saturated porous media [Biot;1956]. Our spatial discretization scheme is based on the three-field formulation (u-w-p) and…

Numerical Analysis · Mathematics 2015-06-24 Zahrasadat Lotfian , Mettupalayam Sivaselvan

In this paper we develop an a priori error analysis of a new unified mixed finite element method for the coupling of fluid flow with porous media flow in $\mathbb{R}^N$, $N\in\{2,3\}$ on isotropic meshes. Flows are governed by the Stokes…

Numerical Analysis · Mathematics 2019-08-07 Koffi Wilfrid Houédanou

We analyze a weak formulation of the coupled problem defining the interac- tion between a free fluid and a poroelastic structure. The problem is fully dynamic and is governed by the time-dependent incompressible Navier-Stokes equations and…

Analysis of PDEs · Mathematics 2022-05-25 Aycil Cesmelioglu

We consider a coupled model of free-flow and porous medium flow, governed by stationary Stokes and Darcy flow, respectively. The coupling between the two systems is enforced by introducing a single variable representing the normal flux…

Numerical Analysis · Mathematics 2022-09-28 Wietse M. Boon

Flow interaction between a plain-fluid region in contact with a porous layer attracted significant attention from modelling and analysis sides due to numerous applications in biology, environment and industry. In the most widely used…

Numerical Analysis · Mathematics 2025-09-03 Linheng Ruan , Iryna Rybak

In this manuscript we focus on the question: what is the correct notion of Stokes-Biot stability? Stokes-Biot stable discretizations have been introduced, independently by several authors, as a means of discretizing Biot's equations of…

Numerical Analysis · Mathematics 2021-04-19 Kent-Andre Mardal , Marie E. Rognes , Travis B. Thompson

In this paper we introduce a finite element method for the Stokes equations with a massless immersed membrane. This membrane applies normal and tangential forces affecting the velocity and pressure of the fluid. Additionally, the points…

Numerical Analysis · Mathematics 2019-05-01 Kyle Dunn , Roger Lui , Marcus Sarkis

A non-conventional shape optimization approach is introduced to address the identification of an obstacle immersed in a fluid described by the Stokes equation within a larger bounded domain, relying on boundary measurements on the…

Optimization and Control · Mathematics 2024-03-19 Julius Fergy Tiongson Rabago , Lekbir Afraites , Hirofumi Notsu

We study decoupled numerical methods for multi-domain, multi-physics applications. By investigating various stages of numerical approximation and decoupling and tracking how the information is transmitted across the interface for a typical…

Numerical Analysis · Mathematics 2019-06-18 Mo Mu , Lian Zhang