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Related papers: Robust space-time multiscale upscaling via multico…

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We derive a new effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by 4-th order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly…

Mathematical Physics · Physics 2013-10-02 Markus Schmuck , Marc Pradas , Greg A. Pavliotis , Serafim Kalliadasis

In this paper, we present the derivation of a multicontinuum model for the coupled flow and transport equations by applying multicontinuum homogenization. We perform the multicontinuum expansion for both flow and transport solutions and…

Numerical Analysis · Mathematics 2024-05-24 Dmitry Ammosov , W. T. Leung , Buzheng Shan , Jian Huang

In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse…

Computational Engineering, Finance, and Science · Computer Science 2023-07-06 Philipp Diercks , Karen Veroy , Annika Robens-Radermacher , Jörg F. Unger

In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…

Numerical Analysis · Mathematics 2022-01-20 Aleksei Tyrylgin , Maria Vasilyeva , Anatoly Alikhanov , Dongwoo Sheen

Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…

Analysis of PDEs · Mathematics 2022-02-01 Stephan Gärttner , Peter Knabner , Nadja Ray

The typical temporal resolution used in modern simulations significantly exceeds characteristic time scales at which the system is driven. This is especially so when systems are simulated over time-scales that are much longer than the…

Fluid Dynamics · Physics 2023-01-09 Farzaneh Rajabi

Our goal of this paper is to develop a new upscaling method for multicontinua flow problems in fractured porous media. We consider a system of equations that describes flow phenomena with multiple flow variables defined on both matrix and…

Numerical Analysis · Mathematics 2018-07-17 Maria Vasilyeva , Eric T. Chung , Siu Wun Cheung , Yating Wang , Georgy Prokopev

An effective macroscopic model for a stochastic microscopic system is derived. The original microscopic system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes or heterogeneities. The…

Analysis of PDEs · Mathematics 2007-05-23 Wei Wang , Daomin Cao , Jinqiao Duan

Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome…

Numerical Analysis · Mathematics 2020-05-15 Xia Wang , Eric Chung , Shubin Fu , Zhaoqin Huang

In this paper, we present a new multiscale model reduction technique for the Stokes flows in heterogeneous perforated domains. The challenge in the numerical simulations of this problem lies in the fact that the solution contains many…

Numerical Analysis · Mathematics 2016-08-26 Eric T. Chung , Maria Vasilyeva , Yating Wang

Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…

Numerical Analysis · Mathematics 2021-08-10 Fabrizio Greco , Lorenzo Leonetti , Paolo Lonetti , Raimondo Luciano , Andrea Pranno

In this article, we study homogenization of a parabolic linear problem governed by a coefficient matrix with rapid spatial and temporal oscillations in periodically perforated domains with homogeneous Neumann data on the boundary of the…

Analysis of PDEs · Mathematics 2018-01-25 Tatiana Lobkova

Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…

Computational Physics · Physics 2021-08-26 Nathan G. March , Elliot J. Carr , Ian W. Turner

In this paper, we propose a rigorous and accurate non-local (in the oversampled region) upscaling framework based on some recently developed multiscale methods [10]. Our proposed method consists of identifying multi-continua parameters via…

Numerical Analysis · Mathematics 2018-08-01 Eric T. Chung , Yalchin Efendiev , Wing Tat Leung , Yating Wang , Maria Vasilyeva

Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum…

Numerical Analysis · Mathematics 2019-06-12 Jun Sur Richard Park , Viet Ha Hoang

Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion…

Applied Physics · Physics 2018-08-01 René Pernas-Salomón , Gal Shmuel

Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within the computational mechanics community for accurate modeling of the deformation, its…

Computational Physics · Physics 2021-04-07 Fanxiang Xu , Hadi Hajibeygi , Lambertus J. Sluys

Understanding processes in porous media is fundamental to a broad spectrum of environmental, energy, and geoscience applications. These processes include multiphase fluid transport, interfacial dynamics, reactive transformations, and…

Fluid Dynamics · Physics 2025-10-08 Na Liu , Jakub Wiktor Both , Geir Ersland , Jan Martin Nordbotten , Martin Fernø

Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…

The paper deals with modelling fluid saturated porous media subject to large deformation. An Eulerian incremental formulation is derived using the problem imposed in the spatial configuration in terms of the equilibrium equation and the…

Numerical Analysis · Mathematics 2018-01-17 Eduard Rohan , Vladimír Lukeš