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The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous piezoelectric structures saturated by Newtonian fluids. The flow is propelled by peristaltic deformation of microchannels which is induced due…

Analysis of PDEs · Mathematics 2024-07-18 Eduard Rohan , Vladimír Lukeš

In this paper, we derive multicontinuum poroelasticity models using the multicontinuum homogenization method. Poroelasticity models are widely used in many areas of science and engineering to describe coupled flow and mechanics processes in…

Numerical Analysis · Mathematics 2025-06-27 Dmitry Ammosov , Mohammed Al-Kobaisi , Yalchin Efendiev

Flow through porous, elastically deforming media is present in a variety of natural contexts ranging from large-scale geophysics to cellular biology. In the case of incompressible constituents, the porefluid pressure acts as a Lagrange…

Fluid Dynamics · Physics 2022-06-30 Nicholas J. Derr , Chris H. Rycroft

We use the local orthogonal decomposition technique to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale diffusion coefficient. We consider nonsmooth initial data and a backward…

Numerical Analysis · Mathematics 2015-05-01 Axel Målqvist , Anna Persson

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

This paper proposes novel computational multiscale methods for linear second-order elliptic partial differential equations in nondivergence-form with heterogeneous coefficients satisfying a Cordes condition. The construction follows the…

Numerical Analysis · Mathematics 2024-07-03 Philip Freese , Dietmar Gallistl , Daniel Peterseim , Timo Sprekeler

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

In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…

Numerical Analysis · Mathematics 2016-09-23 Lorenz Berger

This paper explores an iterative coupling approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order…

Numerical Analysis · Mathematics 2024-01-08 Francesco Ballarin , Sanghyun Lee , Son-Young Yi

In this paper, we study the numerical algorithm for a nonlinear poroelasticity model with nonlinear stress-strain relations. By using variable substitution, the original problem can be reformulated to a new coupled fluid-fluid system, that…

Numerical Analysis · Mathematics 2022-05-17 Zhihao Ge , Hairun Li , Tingting Li

A linear system of differential equations describing a joint motion of thermo-elastic porous body and incompressible thermo-fluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the…

Analysis of PDEs · Mathematics 2007-05-23 Anvarbek M. Meirmanov

We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…

Numerical Analysis · Mathematics 2021-12-13 Per Ljung , Roland Maier , Axel Målqvist

In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use…

Numerical Analysis · Mathematics 2019-09-04 Shubin Fu , Robert Altmann , Eric T. Chung , Roland Maier , Daniel Peterseim , Sai-Mang Pun

We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two-phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated…

Analysis of PDEs · Mathematics 2017-02-13 Michael Eden , Adrian Muntean

When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…

Fluid Dynamics · Physics 2024-10-16 Lucy C Auton , Mohit P. Dalwadi , Ian M. Griffiths

A linear system of differential equations describing a joint motion of thermoelastic porous body and thermofluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main…

Analysis of PDEs · Mathematics 2007-05-23 Anvarbek M. Meirmanov

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…

In this paper, the analysis and homogenization of a poroelastic model for the hydro-mechanical response of fibre-reinforced hydrogels is considered. Here, the medium in question is considered to be a highly heterogeneous two-component media…

Analysis of PDEs · Mathematics 2023-11-27 Michael Eden , Hari Shankar Mahato

We propose and analyze a generalized finite element method designed for linear quasistatic thermoelastic systems with spatial multiscale coefficients. The method is based on the local orthogonal decomposition technique introduced by…

Numerical Analysis · Mathematics 2016-04-04 Axel Målqvist , Anna Persson

We formulate and analyze a multiscale method for an elliptic problem with an oscillatory coefficient based on a skeletal (hybrid) formulation. More precisely, we employ hybrid discontinuous Galerkin approaches and combine them with the…

Numerical Analysis · Mathematics 2025-02-03 Peipei Lu , Roland Maier , Andreas Rupp