Homogenization of the Stokes equations in a domain perforated by a thin truss
Abstract
We consider the homogenization problem of the stationary Stokes equations in a periodically perforated domain whose solid structure consists of a thin truss. That is, the width aε of the truss tends to zero faster than the period size ε. We identify the different scaling regimes and derive the corresponding effective equations. In the critical regime, we obtain the Brinkman equations, while in the subcritical regime, we recover the unchanged Stokes equations. In a subrange of the supercritical regime, we derive Darcy's law as the effective equation. Furthermore, we explicitly compute the effective coefficients in the Darcy and Brinkman limits. Moreover, as a tool in the analysis, we establish the analogous homogenization result for a periodic forest of cylinders. Finally, we also consider the homogenization result for a fence of cylinders.
Related
- Homogenization of an optimal control problem for a Navier-Stokes-Cahn-Hilliard system in a 3D perforated domain
- Critical homogenization of the Navier--Stokes--Cahn--Hilliard system in perforated domains
- Homogenization of degenerate parabolic equations with nonlinear Robin reactions in perforated domains
- Homogenization of the Stokes equations with slender bodies
- From Navier-Stokes to Measure-Valued Euler-Brinkman Equations: Homogenization in the Inviscid Limit
BibTeX
@misc{hadre2026homogenization,
title = {{Homogenization of the Stokes equations in a domain perforated by a thin truss}},
author = {Pascal Hadré and Richard M. Höfer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32804},
eprint = {2610.32804},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32804},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Homogenization of the Stokes equations in a domain perforated by a thin truss
AU - Pascal Hadré
AU - Richard M. Höfer
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.32804
UR - https://arxiv.org/abs/2610.32804
AB - We consider the homogenization problem of the stationary Stokes equations in a periodically perforated domain whose solid structure consists of a thin truss. That is, the width a_ε of the truss tends to zero faster than the period size ε. We identify the different scaling regimes and derive the corresponding effective equations. In the critical regime, we obtain the Brinkman equations, while in the subcritical regime, we recover the unchanged Stokes equations. In a subrange of the supercritical regime, we derive Darcy's law as the effective equation. Furthermore, we explicitly compute the effective coefficients in the Darcy and Brinkman limits. Moreover, as a tool in the analysis, we establish the analogous homogenization result for a periodic forest of cylinders. Finally, we also consider the homogenization result for a fence of cylinders.
ER -