On homogenization of Stokes flow in slowly varying media with applications to fluid-structure interaction

DOI10.1007/s13137-011-0025-yzbMath1255.35029OpenAlexW1976873072MaRDI QIDQ692127

Donald L. Brown, Peter Popov

Publication date: 4 December 2012

Published in: GEM - International Journal on Geomathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13137-011-0025-y

zbMATH Keywords

corrector estimatesalgorithm for computing the correctorsslowly varying geometrytwo scale asymptotic analysis

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Stokes and related (Oseen, etc.) flows (76D07) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Other special methods applied to PDEs (35A25)

Related Items (13)

Multiscale Model Reduction Methods for Flow in Heterogeneous Porous Media ⋮ Homogenization of large deforming fluid-saturated porous structures ⋮ A generalized multiscale finite element method for poroelasticity problems. I: Linear problems. ⋮ A Discontinuous Galerkin Reduced Basis Numerical Homogenization Method for Fluid Flow in Porous Media ⋮ A generalized multiscale finite element method for poroelasticity problems. II: Nonlinear coupling. ⋮ A three-scale offline-online numerical method for fluid flow in porous media ⋮ Application of the asymptotic homogenization in a parametric space to the modeling of structurally heterogeneous materials ⋮ Modeling nonlinear phenomena in deforming fluid-saturated porous media using homogenization and sensitivity analysis concepts ⋮ Double porosity in fluid-saturated elastic media: deriving effective parameters by hierarchical homogenization of static problem ⋮ Effective equations governing an active poroelastic medium ⋮ Acoustics of permeo-elastic materials ⋮ Homogenization of the Navier-Stokes equations by means of the multi-scale virtual power principle ⋮ Homogenization of High-Contrast Brinkman Flows

Cites Work

• Non-homogeneous media and vibration theory
• Homogenisation of a chemical degradation mechanism inducing an evolving microstructure
• Homogenisation in domains with evolving microstructure
• Multiscale Modeling and Simulation of Fluid Flows in Highly Deformable Porous Media
• Multiscale Finite Element Methods
• On Upscaling Certain Flows in Deformable Porous Media
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• Darcy's law for slow viscous flow past a stationary array of bubbles
• The Mathematical Theory of Finite Element Methods
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On homogenization of Stokes flow in slowly varying media with applications to fluid-structure interaction