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Reactive transport in permeable porous media is relevant for a variety of applications, but poses a significant challenge due to the range of length and time scales. Multiscale methods that aim to link microstructure with the macroscopic…

Numerical Analysis · Mathematics 2023-12-27 Mina Karimi , Kaushik Bhattacharya

We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes-Darcy model, in which different time steps can be used in the flow region and in the porous medium. The coupled system is…

Numerical Analysis · Mathematics 2020-07-06 Thi-Thao-Phuong Hoang , Hyesuk Lee

Given a set of inelastic material models, a microstructure, a macroscopic structural geometry, and a set of boundary conditions, one can in principle always solve the governing equations to determine the system's mechanical response.…

Computational Engineering, Finance, and Science · Computer Science 2023-06-27 Ghina Jezdan , Sanjay Govindjee , Klaus Hackl

We present a mixed finite element method for a five-field formulation of the Biot system of poroelasticity that reduces to a cell-centered pressure-displacement system on simplicial and quadrilateral grids. A mixed…

Numerical Analysis · Mathematics 2020-10-28 Ilona Ambartsumyan , Eldar Khattatov , Ivan Yotov

This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…

Numerical Analysis · Mathematics 2024-10-16 Djulustan Nikiforov , Leonardo A. Poveda , Dmitry Ammosov , Yesy Sarmiento , Juan Galvis

Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…

Numerical Analysis · Mathematics 2026-02-26 Yating Wang , Zhengya Yang , Wing Tat Leung

In this paper, we develop a new multiphysics finite element method for a nonlinear poroelastic model with Hencky-Mises stress tensor. By introducing some new notations, we reformulate the original model into a fluid-fluid coupling problem,…

Numerical Analysis · Mathematics 2026-02-24 Yanan He , Zhihao Ge

Stabilized explicit methods are particularly efficient for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they loose their efficiency when a severe stiffness is induced by…

Numerical Analysis · Mathematics 2021-08-13 Assyr Abdulle , Giacomo Rosilho de Souza

This work serves as a primer to our efforts in arriving at convergence estimates for the fixed stress split iterative scheme for single phase flow coupled with small strain anisotropic poroelastoplasticity. The fixed stress split iterative…

Numerical Analysis · Mathematics 2018-10-11 Saumik Dana , Mary F. Wheeler

An efficient, accurate, and flexible numerical method is proposed for the solution of the swimming problem of one or more autophoretic particles in the purely-diffusive limit. The method relies on successive boundary element solutions of…

Fluid Dynamics · Physics 2016-09-13 Thomas D. Montenegro-Johnson , Sebastien Michelin , Eric Lauga

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

In this work, we introduce an iterative linearised finite element method for the solution of Bingham fluid flow problems. The proposed algorithm has the favourable property that a subsequence of the sequence of iterates generated converges…

Numerical Analysis · Mathematics 2021-09-14 Pascal Heid , Endre Süli

We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…

Numerical Analysis · Mathematics 2015-06-22 A. Johansson , J. H. Chaudry , V. Carey , D. Estep , V. Ginting , M. Larson , S. Tavener

Numerical treatment of the problem of two-dimensional viscous fluid flow in and around circular porous inclusions is considered. The mathematical model is described by Navier-Stokes equation in the free flow domain $\Omega_f$ and nonlinear…

Numerical Analysis · Mathematics 2022-09-05 Maria Vasilyeva , S. M. Mallikarjunaiah , D. Palaniappan

This paper is concerned with a blood flow problem coupled with a slow plaque growth at the artery wall. In the model, the micro (fast) system is the Navier-Stokes equation with a periodically applied force and the macro (slow) system is a…

Numerical Analysis · Mathematics 2022-10-21 Zhaoyang Wang , Ping Lin , Lei Zhang

We study a fluid-poroelasticity interaction (FPSI) problem coupling the unsteady Stokes equations with the fully dynamic Biot system. A major challenge in such problems is to design partitioned schemes that remain robust in locking-related…

Numerical Analysis · Mathematics 2026-04-13 Wenlong He , Thomas Wick , Xiaohe Yue , Jiwei Zhang , Haibiao Zheng

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the…

Numerical Analysis · Mathematics 2024-02-19 Ryan M. Aronson , Nicola Castelletto , François P. Hamon , J. A. White , Hamdi A. Tchelepi

This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…

Numerical Analysis · Mathematics 2019-02-06 Graham Baird , Endre Süli

We study a multigrid method for solving large linear systems of equations with tensor product structure. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the…

Numerical Analysis · Mathematics 2017-04-11 Howard C. Elman , Tengfei Su

We analyze a semi-explicit time discretization scheme of first order for poro\-elasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled. The approach leads to a decoupling of…

Numerical Analysis · Mathematics 2021-09-30 Robert Altmann , Roland Maier