A. Abdulle and T. Pouchon, Effective models for the multidimensional wave equation in 806 heterogeneous media over long time and numerical homogenization, Mathematical Models 807 and Methods in Applied Sciences, vol.26, pp.2651-2684, 2016.

A. Abdulle and T. Pouchon, Effective models and numerical homogenization for wave prop-809 agation in heterogeneous media on arbitrary timescales, Foundations of Computational 810 Mathematics, pp.1-43, 2020.

E. Acerbi, V. Chiadopiat, G. Maso, and D. Percivale, An extension theorem from 812 connected sets, and homogenization in general periodic domains, Nonlinear Analysis: The-813 ory, vol.18, pp.481-496, 1992.

G. Allaire, Homogénéisation deséquations de Stokes et de Navier-Stokes, 1989.

G. Allaire, Homogenization of the Stokes flow in a connected porous medium, Asymptotic, vol.817, pp.203-222, 1989.

G. Allaire, Continuity of the Darcy's law in the low-volume fraction limit, Annali della Scuola, vol.819

N. Superiore-di-pisa, Classe di Scienze. Serie IV, vol.18, pp.475-499, 1991.

G. Allaire, Homogenization of the Navier-Stokes equations in open sets perforated with tiny 821 holes I. Abstract framework, a volume distribution of holes, Archive for Rational Mechanics 822 and Analysis, vol.113, pp.209-259, 1991.

G. Allaire, Homogenization of the Navier-Stokes equations with a slip boundary condition, 824 Communications on pure and applied mathematics, vol.44, pp.605-641, 1991.

G. Allaire, Homogenization and two-scale convergence, SIAM Journal on Mathematical, vol.826, pp.1482-1518, 1992.
URL : https://hal.archives-ouvertes.fr/hal-01111805

G. Allaire, Shape optimization by the homogenization method, vol.146, 2012.

G. Allaire and M. Amar, Boundary layer tails in periodic homogenization, ESAIM: Control, 830 Optimisation and Calculus of Variations, vol.4, pp.209-243, 1999.

G. Allaire, M. Briane, and M. Vanninathan, A comparison between two-scale asymp-832 totic expansions and Bloch wave expansions for the homogenization of periodic structures, 833 SEMA journal, vol.73, pp.237-259, 2016.

G. Allaire and C. Conca, Bloch wave homogenization and spectral asymptotic analysis, 835 Journal de mathématiques pures et appliquées, vol.77, pp.153-208, 1998.

G. Allaire, P. Geoffroy-donders, and O. Pantz, Topology optimization of modulated and 837 oriented periodic microstructures by the homogenization method, Computers & Mathemat-838 ics with Applications, 2018.

G. Allaire, A. Lamacz, and J. Rauch, Crime Pays; Homogenized Wave Equations for Long 840 Times, 2018.

G. Allaire and T. Yamada, Optimization of dispersive coefficients in the homogenization of 842 the wave equation in periodic structures, Numerische Mathematik, vol.140, pp.265-326, 2018.

J. Auriault, On the domain of validity of Brinkman's equation, Transp. Porous Media, vol.79, pp.215-223, 2009.

J. Auriault, C. Geindreau, and C. Boutin, Darcy's law, Brinkman's law and poor sepa-846 ration of scales, Proceedings of the 3rd 847 Biot Conference on Poromechanics, pp.553-558, 1905.

N. Bakhvalov and G. Panasenko, Homogenisation: averaging processes in periodic media, of Mathematics and its Applications (Soviet Series), vol.849, 1989.

C. Barbarosie, Shape optimization of periodic structures, Computational Mechanics, vol.30, pp.235-246, 2003.

M. P. Bendsøe and N. Kikuchi, Generating optimal topologies in structural design using 854 a homogenization method, Computer methods in applied mechanics and engineering, vol.71, pp.197-224, 1988.

F. Blanc and S. Nazarov, Asymptotics of solutions to the Poisson problem in a perforated 857 domain with corners, Journal de mathématiques pures et appliquées, vol.76, p.911, 1997.

X. Blanc, C. L. Bris, and P. Lions, Local profiles for elliptic problems at different scales: 860 defects in, and interfaces between periodic structures, Communications in Partial Differ-861 ential Equations, vol.40, pp.2173-2236, 2015.

T. Borrvall and J. Petersson, Large-scale topology optimization in 3D using parallel com-863 puting, Computer methods in applied mechanics and engineering, vol.190, p.6229, 2001.

T. Borrvall and J. Petersson, Topology optimization of fluids in Stokes flow, International 866 Journal for Numerical Methods in Fluids, vol.41, pp.77-107, 2003.

A. Bourgeat, E. Maruvsic-paloka, and A. Mikelic, Weak nonlinear corrections for Darcy's 868 law, Mathematical Models and Methods in Applied Sciences, vol.6, pp.1143-1155, 1996.

K. D. Cherednichenko and J. A. Evans, Full Two-Scale Asymptotic Expansion and Higher-870

, Order Constitutive Laws in the Homogenization of the System of Quasi-static Maxwell 871 Equations, Multiscale Modeling & Simulation, vol.14, pp.1513-1539, 2016.

K. D. Cherednichenko and V. P. Smyshlyaev, On full two-scale expansion of the solutions of 873 nonlinear periodic rapidly oscillating problems and higher-order homogenised variational 874 problems, Archive for rational mechanics and analysis, vol.174, pp.385-442, 2004.

C. Conca, F. Murat, and O. Pironneau, The Stokes and Navier-Stokes equations with 876 boundary conditions involving the pressure, Japanese journal of mathematics. New series, vol.877, issue.20, pp.279-318, 1994.

S. B. Dilgen, C. B. Dilgen, D. R. Fuhrman, O. Sigmund, and B. S. Lazarov, Density 879 based topology optimization of turbulent flow heat transfer systems, Structural and Multi-880 disciplinary Optimization, vol.57, pp.1905-1918, 2018.

A. Ern and J. Guermond, Theory and practice of finite elements, vol.159, 2013.

E. Feireisl and Y. Lu, Homogenization of stationary Navier-Stokes equations in domains 884 with tiny holes, Journal of Mathematical Fluid Mechanics, vol.17, pp.381-392, 2015.

F. Feppon, Shape and topology optimization of multiphysics systems, 2019.
URL : https://hal.archives-ouvertes.fr/tel-02441844

F. Feppon, High order homogenization of the Poisson equation in a perforated periodic domain, Radon Series on Computational and Applied Mathematics, p.889, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02518528

M. Firdaouss, J. Guermond, and P. L. Quéré, Nonlinear corrections to Darcy's law at 890 low Reynolds numbers, Journal of Fluid Mechanics, vol.343, pp.331-350, 1997.

G. P. Galdi, Steady Stokes Flow in Exterior Domains, pp.244-303, 1994.

P. Geoffroy-donders, G. Allaire, and O. Pantz, 3-d topology optimization of modulated 894 and oriented periodic microstructures by the homogenization method, Journal of Compu-895 tational Physics, vol.401, p.108994, 2020.

V. Girault and P. Raviart, Finite element approximation of the Navier-Stokes equations, vol.897, 1979.

J. P. Groen and O. Sigmund, Homogenization-based topology optimization for high-resolution 899 manufacturable microstructures, International Journal for Numerical Methods in Engineer-900 ing, vol.113, pp.1148-1163, 2018.

J. P. Groen, F. C. Stutz, N. Aage, J. A. Baerentzen, and O. Sigmund, De-homogenization 902 of optimal multi-scale 3d topologies, Computer Methods in Applied Mechanics and Engi-903 neering, vol.364, p.112979, 2020.

W. Jing, A unified homogenization approach for the Dirichlet problem in Perforated Domains, 905 arXiv preprint, 2019.

O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, vol.2, 1969.

J. Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal, p.909

, Lecture Notes in Mathematics, vol.323, 1973.

J. Lions, Some methods in the mathematical analysis of systems and their control, 1981.

Y. Lu, Homogenization of stokes equations in perforated domains: a unified approach, 2019.

E. Maruvsic-paloka, Asymptotic expansion for a flow in a periodic porous medium, Comptes, vol.915

, Rendus de l'Academie des Sciences-Series IIB-Mechanics-Physics-Chemistry-Astronomy, vol.916, pp.369-374, 1997.

F. Murat and J. Simon, Sur le contrôle par un domaine géométrique, Publication du Labo-918 ratoire d'Analyse Numérique de l, 1976.

J. Nédélec, Acoustic and electromagnetic equations: integral representations for harmonic 920 problems, 2001.

E. S. Palencia, Non-homogeneous media and vibration theory, Lecture Notes in Physics, vol.127, p.922, 1980.

O. Pantz and K. Trabelsi, A post-treatment of the homogenization method for shape opti-924 mization, SIAM Journal on Control and Optimization, vol.47, pp.1380-1398, 2008.

N. Pollini, O. Sigmund, C. S. Andreasen, and J. Alexandersen, A "poor man's" approach 926 for high-resolution three-dimensional topology design for natural convection problems, Ad-927 vances in Engineering Software, vol.140, p.102736, 2020.

E. Sanchez-palencia, Fluid flow in porous media, Non-homogeneous media and vibration 929 theory, pp.129-157, 1980.

V. P. Smyshlyaev and K. Cherednichenko, On rigorous derivation of strain gradient effects 931 in the overall behaviour of periodic heterogeneous media, Journal of the Mechanics, vol.932, pp.1325-1357, 2000.

L. Tartar, Topics in nonlinear analysis, Publications mathématiques d'Orsay, p.78, 1978.

R. Temam, Navier stokes equations: Theory and numerical analysis, vol.45, 1977.

X. Zhao, M. Zhou, O. Sigmund, and C. Andreasen, A "poor man's approach" to topology 937 optimization of cooling channels based on a Darcy flow model, International Journal of 938 Heat and Mass Transfer, vol.116, pp.1108-1123, 2018.