, Le dispositif expérimental est ensuite placé sur un banc, représenté sur les figures D.22 et D.21. Les différents éléments qui le composent sont : -(1) un bain régulé en température pour maintenir une température d'entrée de fluide à 20°C environ

, ) un réservoir rempli d'eau avec le dispositif expérimental et un échangeur en cuivre à l'intérieur (voir figure D.25)

, Une boîte froide utilisée pour la température de référence des thermocouples. Les thermocouples utilisés sont de type K (Chromel-Alumel), avec une sensibilité de 40 µV ? C ?1 . La température de référence est mesurée par une sonde de platine

, identiques entre les configurations 0 et 2 afin de pouvoir comparer les résultats dans ces deux cas

, Afin de synthétiser les différents résultats obtenus, la puissance évacuée par le fluide Q =?C p ?T est calculée pour chaque débit en comparant les configurations 0 et 2, voir figure D.31. Le ?T est pris entre T1 et T6. Les barres d'erreur sont calculées à l'aide des incertitudes de mesure

, Pour les différents débits étudiés, il y a un gain d'environ 4 W sur la puissance évacuée par le fluide avec la géométrie optimisée à l'intérieur de la cavité

D. Figure, 31 -Comparaison des puissances évacuées (W) par le fluide en fonction du temps (s) pour les différents débits (L/h)

Q. Chen, H. Zhu, N. Pan, and Z. Guo, An alternative criterion in heat transfer optimization, Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences, vol.467, pp.1012-1028, 2011.

A. Bejan, Constructal-theory network of conducting paths for cooling a heat generating volume, International Journal of Heat and Mass Transfer, vol.40, issue.4, pp.799-816, 1997.

A. Bejan, Constructal tree network for fluid flow between a finite-size volume and one source or sink, vol.36, pp.592-604, 1997.

M. Sheikholeslami, M. Gorji-bandpy, and D. Ganji, Review of heat transfer enhancement methods : Focus on passive methods using swirl flow devices, Renewable and Sustainable Energy Reviews, vol.49, pp.444-469, 2015.

L. Gong, K. Kota, W. Tao, and Y. Joshi, Parametric Numerical Study of Flow and Heat Transfer in Microchannels With Wavy Walls, Journal of Heat Transfer, vol.133, issue.5, p.51702, 2011.

C. Fleury, Structural weight optimization by dual methods of convex programming, International Journal for Numerical Methods in Engineering, vol.14, pp.1761-1783, 1979.

J. Céa, Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût, ESAIM : Mathematical Modelling and Numerical Analysis -Modélisation Mathématique et Analyse Numérique, vol.20, issue.3, pp.371-402, 1986.

M. Philip-bendsøe and N. Kikuchi, Computer Methods in Applied Mechanics and Engineering

T. Raphael, Z. Haftka, and . Gürdal, Elements of Structural Optimization, Springer Netherlands, vol.11, 1992.

O. Pironneau, On optimum profiles in stokes flow, Journal of Fluid Mechanics, vol.59, issue.1, pp.117-128, 1973.

G. Allaire, F. Jouve, and A. Toader, A level-set method for shape optimization, Comptes Rendus Mathematique, vol.334, issue.12, pp.1125-1130, 2002.
URL : https://hal.archives-ouvertes.fr/hal-01336301

L. Wang, Y. Fan, and L. Luo, Lattice Boltzmann method for shape optimization of fluid distributor, Computers & Fluids, vol.94, pp.49-57, 2014.

G. Allaire, F. Jouve, and A. Toader, Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, pp.363-393, 2004.

M. Philip-bendsoe and O. Sigmund, Topology Optimization : Theory, Methods and Applications, 2004.

O. Sigmund, A 99 line topology optimization code written in Matlab. Structural and Multidisciplinary Optimization, vol.21, pp.120-127, 2001.

G. Marck, Topological Optimization of Heat and Mass Transfer, 2012.
URL : https://hal.archives-ouvertes.fr/pastel-00819099

M. Stolpe and K. Svanberg, An alternative interpolation scheme for minimum compliance topology optimization. Structural and Multidisciplinary Optimization, vol.22, pp.116-124, 2001.

S. Wang, K. Tai, and M. Y. Wang, An enhanced genetic algorithm for structural topology optimization, International Journal for Numerical Methods in Engineering, vol.65, issue.1, pp.18-44, 2005.

V. J. Challis, A discrete level-set topology optimization code written in Matlab. Structural and Multidisciplinary Optimization, vol.41, pp.453-464, 2009.

G. Rozvany, A critical review of established methods of structural topology optimization. Structural and Multidisciplinary Optimization, vol.37, pp.217-237, 2008.

Y. Michael, X. Wang, D. Wang, and . Guo, A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.1-2, pp.227-246, 2003.

T. Dbouk, A review about the engineering design of optimal heat transfer systems using topology optimization, Applied Thermal Engineering, 2016.

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

A. Gersborg-hansen, Topology optimization of incompressible Newtonian flows at moderate Reynolds numbers, 2003.

J. Vivien, J. K. Challis, and . Guest, Level set topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Engineering, vol.79, issue.10, pp.1284-1308, 2009.

J. K. Guest and J. H. Prévost, Topology optimization of creeping fluid flows using a Darcy-Stokes finite element, International Journal for Numerical Methods in Engineering, vol.66, pp.461-484, 2006.

G. Pingen, M. Waidmann, A. Evgrafov, and K. Maute, A parametric levelset approach for topology optimization of flow domains. Structural and Multidisciplinary Optimization, vol.41, pp.117-131, 2009.

S. Kreissl, K. Pingen, and . Maute, Topology optimization for unsteady flow, International Journal for Numerical Methods in Engineering, vol.87, pp.1229-1253, 2011.

G. Marck, M. Nemer, J. Harion, S. Russeil, and D. Bougeard, Evolutionary structural optimization by extension to cool a finite-size volume generating heat, 7th International Conference on Computational Heat and Mass Transfer, 2011.

A. Gersborg-hansen, M. P. Bendsøe, and O. Sigmund, Topology optimization of heat conduction problems using the finite volume method. Structural and Multidisciplinary Optimization, vol.31, pp.251-259, 2006.

Y. M. Xie, Q. Li, O. M. Querin, and G. P. Steven, Shape and topology design for heat conduction by Evolutionary Structural Optimization, International Journal of Heat and Mass Transfer, vol.42, pp.3361-3371, 1999.

G. Ho-yoon, Topological design of heat dissipating structure with forced convective heat transfer, Journal of Mechanical Science and Technology, vol.24, issue.6, pp.1225-1233, 2010.

J. Alexandersen, Topology Optimisation for Coupled Convection Problems, 2013.

K. Yaji, T. Yamada, M. Yoshino, T. Matsumoto, K. Izui et al., Topology optimization in thermal-fluid flow using the lattice Boltzmann method, Journal of Computational Physics, vol.307, pp.355-377, 2016.

Y. Favennec, L. Masson, and Y. Jarny, Lecture 7 : Optimization methods for non linear estimation and function estimation, Thermal measurements and inverse techniques, 2011.

O. Sigmund and K. Maute, Topology optimization approaches. Structural and Multidisciplinary Optimization, vol.48, pp.1031-1055, 2013.

B. Michael, N. A. Giles, and . Pierce, An introduction to the adjoint approach to design. Flow, Turbulence and Combustion, vol.65, pp.393-415, 2000.

A. M. Bradley, PDE-constrained optimization problems and the adjoint method, vol.2012, pp.1-6, 2012.

A. Jameson, Aerodynamic design via control theory, Journal of Scientific Computing, vol.3, issue.3, pp.233-260, 1988.

R. M. Errico, What Is an Adjoint Model ?, Bulletin of the American Meteorological Society, vol.78, issue.11, pp.2577-2591, 1997.

G. Steven and . Johnson, Notes on Adjoint Methods, 2007.

S. Osher and J. Sethian, Front propagating with courvature-dependent speed : algorithms based on hamilton-Jacoby formulations, J. Computational physics, vol.79, pp.12-49, 1988.

P. J-a-sethian and . Smereka, Level Set Methods for Fluid Interfaces, Annual Review of Fluid Mechanics, vol.35, pp.341-372, 2003.

D. A. Wolf-gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models -An Introduction. PoLAR, p.308, 2000.

Z. Guo and C. Shu, Lattice Boltzmann method and its applications in engineering, vol.54, 2013.

S. Marié, Etude de la méthode Boltzmann sur Réseau pour les simulations en aéroacoustique, 2008.

L. Jonas, Hydrodynamic Limit of Lattice Boltzmann Equations, 2007.

A. A. Mohamad, Lattice Boltzmann Method -Fundamentals and Engineering Applications with computer codes, 2011.

L. Wang, Y. Fan, and L. Luo, Heuristic optimality criterion algorithm for shape design of fluid flow, Journal of Computational Physics, vol.229, issue.20, pp.8031-8044, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00516148

N. Delbosc, Real-Time Simulation of Indoor Air Flow Using the Lattice Boltzmann Method on Graphics Processing Unit, 2015.

A. Adriano, E. Koga, C. Comini, . Lopes, F. Helcio et al., Development of heat sink device by using topology optimization, International Journal of Heat and Mass Transfer, vol.64, pp.759-772, 2013.

L. Luo, M. Wei, Y. Fan, and G. Flamant, Heuristic shape optimization of baffled fluid distributor for uniform flow distribution, Chemical Engineering Science, vol.123, pp.542-556, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01175587

C. Pistoresi, Y. Fan, and L. Luo, Numerical study on the improvement of flow distribution uniformity among parallel mini-channels, Process Intensification, vol.95, pp.63-71, 2015.

R. Boichot, L. Luo, and Y. Fan, Tree-network structure generation for heat conduction by cellular automaton. Energy Conversion and Management, vol.50, pp.376-386, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00452756

Y. Favennec, L. Dubot, . Hardy, and . Rousseau, Space-dependent Sobolev gradients as a regularization for inverse radiative transfer problems

G. Pingen, Optimal Design for Fluidic Systems : Topology and Shape Optimization with the Lattice Boltzmann Method, 2008.

G. Delgado, Optimization of composite structures : A shape and topology sensitivity analysis, 2014.
URL : https://hal.archives-ouvertes.fr/pastel-01005520

A. Hans, N. Eschenauer, and . Olhoff, Topology optimization of continuum structures : A review, Applied Mechanics Reviews, vol.54, issue.4, p.331, 2001.

M. Gunzburger, Adjoint equation-based methods for control problems in incompressible, viscous flows. Flow, Turbulence and Combustion, vol.65, pp.249-272, 2000.

J. Nocedal and S. J. Wright, Numerical Optimization, 2006.

A. Dieter and . Wolf-gladrow, Lattice Gas Cellular Automata and Lattice Boltzmann Models, volume 1725 of Lecture Notes in Mathematics, 2000.

Y. M. Xie and G. P. Steven, A simple evolutionary procedure for structural optimization, Computers & Structures, vol.49, issue.5, pp.885-896, 1993.

C. Zhao, G. P. Steven, and Y. M. Xie, Evolutionary natural frequency optimization of thin plate bending vibration problems. Structural optimization, vol.11, pp.244-251, 1996.

D. J. Munk, G. A. Vio, and G. P. Steven, Topology and shape optimization methods using evolutionary algorithms : a review. Structural and Multidisciplinary Optimization, 2015.

X. Huang and Y. M. Xie, Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elements in Analysis and Design, vol.43, pp.1039-1049, 2007.

O. Sigmund, On the usefulness of non-gradient approaches in topology optimization. Structural and Multidisciplinary Optimization, vol.43, pp.589-596, 2011.

M. Mitchell, An Introduction to Genetic Algorithms, 1996.

R. and J. Kennedy, A new optimizer using particle swarm theory, Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp.39-43, 1995.

C. Y. Guan-chun-luh, Y. S. Lin, and . Lin, A binary particle swarm optimization for continuum structural topology optimization, Applied Soft Computing Journal, vol.11, issue.2, pp.2833-2844, 2011.

P. J. Laarhoven and E. H. Aarts, Simulated Annealing : Theory and Applications, 1987.

Y. Patrick, S. Shim, and . Manoochehri, Generating optimal configurations in structural design using simulated annealing, International Journal for Numerical Methods in Engineering, vol.40, issue.6, pp.1053-1069, 1997.

R. Balamurugan, C. V. Ramakrishnan, and N. Singh, Performance evaluation of a two stage adaptive genetic algorithm (TSAGA) in structural topology optimization, Applied Soft Computing, vol.8, issue.4, pp.1607-1624, 2008.

R. Balamurugan, C. V. Ramakrishnan, and N. Swaminathan, A two phase approach based on skeleton convergence and geometric variables for topology optimization using genetic algorithm. Structural and Multidisciplinary Optimization, vol.43, pp.381-404, 2011.

M. Bergounioux, Optimisation et contrôle des systèmes linéaires. Dunod, 2001.

M. Bergmann, ;. Jean-pierre, and . Cordier, Optimisation aérodynamique par réduction de modèle POD et contrôle optimal : application au sillage laminaire d'un cylindre circulaire, Laurent Mécanique des fluides Vandoeuvre-les-Nancy, 2004.

, Computational Fluid Dynamics. Optimization and Computational Fluid Dynamics, 2008.

M. Bierlaire, Introduction à l'optimisation différentiable, 2005.

M. Bergmann, L. Cordier, and J. P. Brancher, Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced-order model, Physics of Fluids, vol.17, issue.9, pp.1-21, 2005.

S. Y. Wang, K. M. Lim, B. C. Khoo, and M. Y. Wang, An extended level set method for shape and topology optimization, Journal of Computational Physics, vol.221, issue.1, pp.395-421, 2007.

S. Wang and M. Y. Wang, Radial basis functions and level set method for structural topology optimization, International Journal for Numerical Methods in Engineering, vol.65, issue.12, pp.2060-2090, 2006.

S. Zhou and Q. Li, A variational level set method for the topology optimization of steady-state Navier-Stokes flow, Journal of Computational Physics, vol.227, issue.24, pp.10178-10195, 2008.

W. Peter, A. Christensen, and . Klarbring, An Introduction to Structural Optimization, Solid Mechanics and Its Applications, vol.153, 2008.

C. Fleury, CONLIN : An efficient dual optimizer based on convex approximation concepts, Structural Optimization, vol.1, issue.2, pp.81-89, 1989.

K. Svanberg, The method of moving asymptotes-a new method for structural optimization, International Journal for Numerical Methods in Engineering, vol.24, pp.359-373, 1987.

K. Svanberg, A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations, 2002.

M. P. Bendsøe, Optimal shape design as a material distribution problem, Structural Optimization, vol.1, issue.4, pp.193-202, 1989.

N. P. Van-dijk, K. Maute, M. Langelaar, and F. Van-keulen, Level-set methods for structural topology optimization : a review. Structural and Multidisciplinary Optimization, vol.48, pp.437-472, 2013.

L. P. Kong-tian-zuo, Y. Q. Chen, J. Zhang, and . Yang, Study of key algorithms in topology optimization, International Journal of Advanced Manufacturing Technology, vol.32, issue.7-8, pp.787-796, 2007.

T. Yamada, K. Izui, S. Nishiwaki, and A. Takezawa, A topology optimization method based on the level set method incorporating a fictitious interface energy, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.2876-2891, 2010.

S. Osher and N. Paragios, Geometric Level Set Methods in Imaging,Vision,and Graphics, 2003.

A. James, A. Sethian, and . Wiegmann, Structural Boundary Design via Level Set and Immersed Interface Methods, Journal of Computational Physics, vol.163, pp.489-528, 2000.

. G-allaire, F. De-gournay, A. Jouve, and . Toader, Structural optimization using topological and shape sensitivity via a level set method, Control and cybernetics, vol.34, p.59, 2004.

S. Amstutz and H. Andrä, A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, vol.216, pp.573-588, 2006.

X. Duan, Y. Ma, and R. Zhang, Shape-topology optimization of stokes flow via variational level set method, Applied Mathematics and Computation, vol.202, issue.1, pp.200-209, 2008.

C. Zhuang, Z. Xiong, and H. Ding, A level set method for topology optimization of heat conduction problem under multiple load cases, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.4-6, pp.1074-1084, 2007.

P. Coffin and K. Maute, Level set topology optimization of cooling and heating devices using a simplified convection model. Structural and Multidisciplinary Optimization, vol.53, pp.985-1003, 2016.

M. Otomori, T. Yamada, K. Izui, and S. Nishiwaki, Matlab code for a level set-based topology optimization method using a reaction diffusion equation. Structural and Multidisciplinary Optimization, pp.1159-1172, 2014.

K. Yaji, T. Yamada, M. Yoshino, T. Matsumoto, K. Izui et al., Topology optimization using the lattice Boltzmann method incorporating level set boundary expressions, Journal of Computational Physics, vol.274, pp.158-181, 2014.

K. Yaji, T. Yamada, S. Kubo, K. Izui, and S. Nishiwaki, A topology optimization method for a coupled thermal-fluid problem using level set boundary expressions, International Journal of Heat and Mass Transfer, 2014.

D. Guirguis and M. F. Aly, A derivative-free level-set method for topology optimization, Finite Elements in Analysis and Design, vol.120, pp.41-56, 2016.

M. Burger, B. Hackl, and W. Ring, Incorporating topological derivatives into level set methods, Journal of Computational Physics, vol.194, issue.1, pp.344-362, 2004.

G. Frédéric-de, Optimisation de formes par la méthode des lignes de niveaux, 2003.

N. P. Van-dijk, M. Langelaar, and F. Van-keulen, Explicit level-set-based topology optimization using an exact heaviside function and consistent sensitivity analysis, International Journal for Numerical Methods in Engineering, vol.91, issue.1, pp.67-97, 2012.

P. Wei, Z. Li, X. Li, and M. Y. Wang, An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions. Structural and Multidisciplinary Optimization, 2018.

J. Luo, Z. Luo, S. Chen, L. Tong, and M. Y. Wang, A new level set method for systematic design of hinge-free compliant mechanisms, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.2, pp.318-331, 2008.

K. S-y-wang, B. Lim, M. Khoo, and . Wang, On hole nucleation in topology optimization using the level set methods, Computer Modeling in Engineering and Sciences, vol.21, issue.3, p.219, 2007.

L. Arun, . Gain, H. Glaucio, and . Paulino, A critical comparative assessment of differential equation-driven methods for structural topology optimization. Structural and Multidisciplinary Optimization, vol.48, pp.685-710, 2013.

Z. Luo, L. Tong, M. Y. Wang, and S. Wang, Shape and topology optimization of compliant mechanisms using a parameterization level set method, Journal of Computational Physics, vol.227, issue.1, pp.680-705, 2007.

J. Sokolowski and A. Zochowski, On the Topological Derivative in Shape Optimization, SIAM Journal on Control and Optimization, vol.37, issue.4, pp.1251-1272, 1999.

J. Céa, S. Garreau, P. Guillaume, and M. Masmoudi, The shape and topological optimizations connection, Computer Methods in Applied Mechanics and Engineering, vol.188, issue.4, pp.713-726, 2000.

S. Garreau, P. Guillaume, and M. Masmoudi, The Topological Asymptotic for PDE Systems : The Elasticity Case, SIAM Journal on Control and Optimization, vol.39, issue.6, pp.1756-1778, 2001.

A. A. Novotny, R. A. Feijóo, E. Taroco, and C. Padra, Topological sensitivity analysis, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.7-8, pp.803-829, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00861461

J. A. Norato, M. P. Bendsøe, R. B. Haber, and D. A. Tortorelli, A topological derivative method for topology optimization. Structural and Multidisciplinary Optimization, vol.33, pp.375-386, 2007.

S. Kreissl, K. Pingen, and . Maute, An explicit level set approach for generalized shape optimization of fluids with the lattice Boltzmann method, International Journal for Numerical Methods in Fluids, vol.65, pp.496-519, 2011.

S. Amstutz, Connections between topological sensitivity analysis and material interpolation schemes in topology optimization. Structural and Multidisciplinary Optimization, vol.43, pp.755-765, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01325799

X. Guo, K. Zhao, and M. Y. Wang, A new approach for simultaneous shape and topology optimization based on implicit topology description functions, Proceedings of the ASME Design Engineering Technical Conference, vol.1, pp.503-512, 2004.

T. Yamada, K. Izui, and S. Nishiwaki, A Level Set-Based Topology Optimization Method for Maximizing Thermal Diffusivity in Problems Including Design-Dependent Effects, Journal of Mechanical Design, vol.133, issue.3, p.31011, 2011.

A. Gersborg-hansen, O. Sigmund, and R. B. Haber, Topology optimization of channel flow problems. Structural and Multidisciplinary Optimization, vol.30, pp.181-192, 2005.

A. Evgrafov, Topology optimization of slightly compressible fluids, ZAMM, vol.86, issue.1, pp.46-62, 2006.

Y. Deng, Z. Liu, P. Zhang, Y. Liu, and Y. Wu, Topology optimization of unsteady incompressible Navier-Stokes flows, Journal of Computational Physics, vol.230, issue.17, pp.6688-6708, 2011.

G. Pingen, A. Evgrafov, and K. Maute, Adjoint parameter sensitivity analysis for the hydrodynamic lattice Boltzmann method with applications to design optimization

, Computers & Fluids, vol.38, issue.4, pp.910-923, 2009.

T. E. Bruns, Topology optimization of convection-dominated, steady-state heat transfer problems, International Journal of Heat and Mass Transfer, vol.50, pp.2859-2873, 2007.

E. Dede, Multiphysics topology optimization of heat transfer and fluid flow systems, COMSOL Conference, 2009.

G. Marck, M. Nemer, and J. L. Harion, Topology Optimization of Heat and Mass Transfer Problems : Laminar Flow, Numerical Heat Transfer, vol.63, pp.508-539, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00880111

T. Matsumori, T. Kondoh, A. Kawamoto, and T. Nomura, Topology optimization for fluid-thermal interaction problems under constant input power. Structural and Multidisciplinary Optimization, vol.47, pp.571-581, 2013.

M. Zhou, J. Alexandersen, O. Sigmund, and C. B. Claus, Industrial application of topology optimization for combined conductive and convective heat transfer problems. Structural and Multidisciplinary Optimization, vol.54, pp.1045-1060, 2016.

K. Lee, Topology optimization of convective cooling system designs, 2012.

T. Van-oevelen and M. Baelmans, Application of topology optimization in a conjugate heat transfer problem, pp.4-6, 2014.

E. A. Kontoleontos, E. M. Papoutsis-kiachagias, A. S. Zymaris, D. I. Papadimitriou, and K. C. Giannakoglou, Adjoint-based constrained topology optimization for viscous flows, including heat transfer. Engineering Optimization, vol.45, issue.8, pp.941-961, 2013.

P. Coffin and K. Maute, A level-set method for steady-state and transient natural convection problems. Structural and Multidisciplinary Optimization, vol.53, pp.1047-1067, 2016.

G. Pingen and D. Meyer, Topology optimization for thermal transport, 2009.

M. M. Tekitek, M. Bouzidi, F. Dubois, and P. Lallemand, Adjoint lattice Boltzmann equation for parameter identification, Computers & Fluids, vol.35, issue.8-9, pp.805-813, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01016184

A. Kirk, S. Kreissl, G. Pingen, and K. Maute, Lattice Boltzmann Topology Optimization for Transient Flow, MAESC 2011 Conference, pp.1-8, 2011.

K. Yonekura and Y. Kanno, A flow topology optimization method for steady state flow using transient information of flow field solved by lattice Boltzmann method. Structural and Multidisciplinary Optimization, vol.51, pp.159-172, 2014.

S. Nørgaard, O. Sigmund, and B. Lazarov, Topology optimization of unsteady flow problems using the lattice Boltzmann method, Journal of Computational Physics, vol.307, pp.291-307, 2016.

M. J. Krause, G. Thäter, and V. Heuveline, Adjoint-based fluid flow control and optimisation with lattice Boltzmann methods, Computers and Mathematics with Applications, vol.65, pp.945-960, 2013.

G. Liu, M. Geier, Z. Liu, M. Krafczyk, and T. Chen, Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice Boltzmann method, Computers & Mathematics with Applications, vol.68, issue.10, pp.1374-1392, 2014.

Q. Zou and X. He, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Physics of Fluids, vol.9, p.1591, 1997.

L. Laniewski-wollk and J. Rokicki, Adjoint lattice boltzmann for topology optimization on multi-gpu architecture, Computers & Mathematics with Applications, vol.71, issue.3, pp.833-848, 2016.

E. Vergnault and P. Sagaut, An adjoint-based lattice Boltzmann method for noise control problems, Journal of Computational Physics, vol.276, pp.39-61, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01293343

X. He and L. Luo, Lattice Boltzmann Model for the Incompressible Navier-Stokes Equation, Journal of Statistical Physics, vol.88, pp.927-944, 1997.

D. Lagrava, O. Malaspinas, J. Latt, and B. Chopard, Advances in multi-domain lattice Boltzmann grid refinement, Journal of Computational Physics, vol.231, issue.14, pp.4808-4822, 2012.

M. Gad-el-hak, The Fluid Mechanics of Microdevices-The Freeman Scholar Lecture, Journal of Fluids Engineering, vol.121, issue.1, 1999.

R. K. Agarwal, K. Yun, and R. Balakrishnan, Beyond Navier-Stokes : Burnett equations for flows in the continuum-transition regime, Physics of Fluids, vol.13, issue.10, p.3061, 2001.

N. T. Nguyen and S. T. Wereley, Fundamentals and Applications of Microfluidics. Artech House integrated microsystems series, 2006.

M. Allen, Computational Soft Matter : From Synthetic Polymers to, Proteins, vol.23, issue.2, pp.1-28, 2004.

D. Mewes and F. Mayinger, Direct Simulation Monte-Carlo (DSMC) Method, pp.275-315, 2005.

S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Numerical Mathematics and Scientific Computation). Numerical mathematics and scientific computation, 2001.

Z. Guo and T. S. Zhao, Lattice Boltzmann model for incompressible flows through porous media, Physical Review E -Statistical, Nonlinear, and Soft Matter Physics, vol.66, issue.3, 2002.

D. Gao, Z. Chen, L. Chen, and D. Zhang, A modified lattice Boltzmann model for conjugate heat transfer in porous media, International Journal of Heat and Mass Transfer, vol.105, pp.673-683, 2017.

H. Yu, L. Shi-luo, and S. S. Girimaji, LES of turbulent square jet flow using an MRT lattice Boltzmann model, Computers and Fluids, vol.35, issue.8-9, pp.957-965, 2006.

P. Sagaut, Toward advanced subgrid models for Lattice-Boltzmann-based Large-eddy simulation : Theoretical formulations, Computers and Mathematics with Applications, vol.59, issue.7, pp.2194-2199, 2010.

Z. Guo, B. Shi, and C. Zheng, A coupled lattice BGK model for the Boussinesq equations, International Journal for Numerical Methods in Fluids, vol.39, issue.4, pp.325-342, 2002.

X. He, S. Chen, and G. D. Doolen, A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit, Journal of Computational Physics, vol.146, issue.1, pp.282-300, 1998.

C. Subhash, A. Mishra, K. N. Lankadasu, and . Beronov, Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction-radiation problem, International Journal of Heat and Mass Transfer, vol.48, issue.17, pp.3648-3659, 2005.

X. Shan and H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components, Physical Review E, vol.47, issue.3, pp.1815-1819, 1993.

H. Liu, Q. Kang, C. R. Leonardi, S. Schmieschek, A. Narváez et al., Multiphase lattice Boltzmann simulations for porous media applications, Computational Geosciences, vol.20, issue.4, pp.777-805, 2016.

J. Hardy, Y. De-pazzis, and . Pomeau, Molecular dynamics of a classical lattice gas : Transport properties and time correlation functions, vol.13, 1976.

U. Frisch, B. Hasslacher, and Y. Pomeau, Lattice-Gas Automata for the Navier-Stokes Equation, Physical Review Letters, vol.56, issue.14, pp.1505-1508, 1986.

. Bastien-chopard, Cellular Automata Modeling of Physical Systems, pp.865-892, 2009.

C. Michael, D. T. Sukop, and . Thorne, Lattice boltzmann modeling : An introduction for geoscientists and engineers, 2006.

D. Ricot, Simulation numérique d'un écoulement affleurant une cavité par la méthode Boltzmann sur Réseau et application au toit ouvrant de véhicules automobiles, 2002.

C. Cercignani, The Boltzmann Equation and Its Applications. Number, vol.67, 1988.

X. He and L. Luo, A priori derivation of the lattice Boltzmann equation, Physical Review E, vol.55, issue.6, pp.6333-6336, 1997.

P. Bhatnagar, E. Gross, and M. Krook, A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems, Physical Review, vol.94, issue.3, pp.511-525, 1954.

I. Dominique-d'humières, M. Ginzburg, P. Krafczyk, L. Lallemand, and . Luo, Multiple-relaxation-time lattice Boltzmann models in three dimensions, Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, vol.360, pp.437-451, 1792.

X. Shan and X. He, Discretization of the velocity space in the solution of the boltzmann equation, Phys. Rev. Lett, vol.80, pp.65-68, 1998.

X. He and L. Luo, Theory of the lattice boltzmann method : From the boltzmann equation to the lattice boltzmann equation, Phys. Rev. E, vol.56, pp.6811-6817, 1997.

R. W. Nash, H. B. Carver, M. O. Bernabeu, J. Hetherington, D. Groen et al., Choice of boundary condition for lattice-boltzmann simulation of moderate-reynolds-number flow in complex domains, Phys. Rev. E, vol.89, p.23303, 2014.

R. S. Maier, R. S. Bernard, and D. W. Grunau, Boundary conditions for the lattice Boltzmann method, Physics of Fluids, vol.8, issue.7, p.1788, 1996.

L. Jahanshaloo, . Nor-azwadi-che, A. Sidik, M. Fazeli, and H. A. Pesaran, An overview of boundary implementation in lattice Boltzmann method for computational heat and mass transfer. International Communications in Heat and Mass Transfer, 2016.

S. Chen, D. Martínez, and R. Mei, On boundary conditions in lattice Boltzmann methods, Physics of Fluids, vol.8, issue.9, pp.2527-2536, 1996.

C. Joris and . Verschaeve, Analysis of the lattice Boltzmann Bhatnagar-Gross-Krook no-slip boundary condition : Ways to improve accuracy and stability, Physical Review E -Statistical, Nonlinear, and Soft Matter Physics, vol.80, pp.1-23, 2009.

X. He, Q. Zou, L. Luo, and M. Dembo, Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model, Journal of Statistical Physics, vol.87, issue.1-2, pp.115-136, 1997.

Q. Zou, S. Hou, S. Chen, and G. D. Doolen, A improved incompressible lattice Boltzmann model for time-independent flows, Journal of Statistical Physics, vol.81, issue.1-2, pp.35-48, 1995.

G. Mcnamara and B. Alder, Analysis of the lattice Boltzmann treatment of hydrodynamics, Physica A : Statistical Mechanics and its Applications, vol.194, issue.1-4, pp.218-228, 1993.

F. Alexander, S. Chen, and J. Sterling, Lattice Boltzmann thermohydrodynamics, Physical Review E, vol.47, issue.4, pp.2249-2252, 1993.

R. Guy, A. L. Mcnamara, B. J. Garcia, and . Alder, A hydrodynamically correct thermal lattice Boltzmann model, Journal of Statistical Physics, vol.87, issue.5-6, pp.1111-1121, 1997.

R. Guy, A. L. Mcnamara, B. J. Garcia, and . Alder, Stabilization of thermal lattice Boltzmann models, Journal of Statistical Physics, vol.81, issue.1-2, pp.395-408, 1995.

C. Obrecht, F. Kuznik, B. Tourancheau, and J. J. Roux, The TheLMA project : A thermal lattice Boltzmann solver for the GPU, Computers and Fluids, vol.54, issue.1, pp.118-126, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00731135

A. Mezrhab, P. Bouzidi, and . Lallemand, Hybrid lattice-Boltzmann finitedifference simulation of convective flows, Computers & Fluids, vol.33, issue.4, pp.623-641, 2004.

C. Subhash, H. K. Mishra, and . Roy, Solving transient conduction and radiation heat transfer problems using the lattice Boltzmann method and the finite volume method, Journal of Computational Physics, vol.223, issue.1, pp.89-107, 2007.

Y. Ma, S. Dong, and H. Tan, Lattice Boltzmann method for one-dimensional radiation transfer, Physical Review E -Statistical, Nonlinear, and Soft Matter Physics, vol.84, issue.1, pp.1-5, 2011.

H. Yi, F. Yao, and H. Tan, Lattice Boltzmann model for a steady radiative transfer equation, Physical Review E, vol.94, issue.2, p.23312, 2016.

K. Lin, C. Liao, S. Lien, and C. Lin, Thermal lattice Boltzmann simulations of natural convection with complex geometry, Computers & Fluids, vol.69, pp.35-44, 2012.

L. Li, R. Mei, and J. F. Klausner, Lattice Boltzmann models for the convectiondiffusion equation : D2Q5 vs D2Q9, International Journal of Heat and Mass Transfer, vol.108, pp.41-62, 2017.

Z. Li, M. Yang, and Y. Zhang, A coupled lattice Boltzmann and finite volume method for natural convection simulation, International Journal of Heat and Mass Transfer, vol.70, pp.864-874, 2014.

T. Inamuro, Lattice Boltzmann methods for viscous fluid flows and for two-phase fluid flows, Fluid Dynamics Research, vol.38, issue.9, pp.641-659, 2006.

Y. Chen, H. Ohashi, and M. Akiyama, Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamic equations, Physical Review E, vol.50, issue.4, pp.2776-2783, 1994.

Y. Peng, C. Shu, and Y. Chew, Simplified thermal lattice Boltzmann model for incompressible thermal flows, Physical Review E, vol.68, issue.2, p.26701, 2003.

Y. Shi, T. Zhao, and Z. Guo, Thermal lattice Bhatnagar-Gross-Krook model for flows with viscous heat dissipation in the incompressible limit, Physical Review E, vol.70, issue.6, p.66310, 2004.

G. Tang, W. Tao, and Y. He, Thermal boundary condition for the thermal lattice Boltzmann equation, Physical Review E, vol.72, issue.1, p.16703, 2005.

C. Liu, K. Lin, H. Mai, and C. Lin, Thermal boundary conditions for thermal lattice Boltzmann simulations, Computers & Mathematics with Applications, vol.59, issue.7, pp.2178-2193, 2010.

L. Li, R. Mei, and J. F. Klausner, Boundary conditions for thermal lattice Boltzmann equation method, Journal of Computational Physics, vol.237, pp.366-395, 2013.

D. Annunziata and S. Succi, Simulating two-dimensional thermal channel flows by means of a lattice Boltzmann method with new boundary conditions, Future Generation Computer Systems, vol.20, issue.6, pp.935-944, 2004.

T. Inamuro, M. Yoshino, and F. Ogino, A non-slip boundary condition for lattice Boltzmann simulations, Physics of Fluids, vol.7, issue.8, 1995.

T. Inamuro, M. Yoshino, H. Inoue, R. Mizuno, and F. Ogino, A Lattice Boltzmann Method for a Binary Miscible Fluid Mixture and Its Application to a Heat-Transfer Problem, Journal of Computational Physics, vol.179, pp.201-215, 2002.

M. Hecht and J. Harting, Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann simulations, Journal of Statistical Mechanics : Theory and Experiment, issue.01, p.1018, 2010.

A. Mezrhab, M. A. Moussaoui, M. Jami, H. Naji, and M. Bouzidi, Double MRT thermal lattice Boltzmann method for simulating convective flows, Physics Letters A, vol.374, issue.34, pp.3499-3507, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00512643

H. Yoshida and M. Nagaoka, Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation, Journal of Computational Physics, vol.229, issue.20, pp.7774-7795, 2010.

Q. Liu, Y. He, Q. Li, and W. Tao, A multiple-relaxation-time lattice Boltzmann model for convection heat transfer in porous media, International Journal of Heat and Mass Transfer, vol.73, pp.761-775, 2014.

J. Wang, D. Wang, P. Lallemand, and L. Luo, Lattice Boltzmann simulations of thermal convective flows in two dimensions, Computers & Mathematics with Applications, vol.65, issue.2, pp.262-286, 2013.

F. Dubois, Une introduction au schéma de boltzmann sur réseau, ESAIM : Proc, vol.18, pp.181-215, 2007.

D. Dominique and . Humières, Multiple-relaxation-time lattice Boltzmann models in three dimensions, pp.437-451, 2002.

M. Geier, A. Greiner, and J. G. Korvink, Cascaded digital lattice boltzmann automata for high reynolds number flow. Physical review. E, Statistical, nonlinear, and soft matter physics, vol.73, p.66705, 2006.

M. Geier, M. Schönherr, A. Pasquali, and M. Krafczyk, The cumulant lattice Boltzmann equation in three dimensions : Theory and validation, Computers and Mathematics with Applications, vol.70, issue.4, pp.507-547, 2015.

M. Geier, A. Greiner, and J. G. Korvink, A factorized central moment lattice Boltzmann method, European Physical Journal : Special Topics, vol.171, issue.1, pp.55-61, 2009.

M. Bouzidi, M. Firdaouss, and P. Lallemand, Momentum transfer of a Boltzmann-lattice fluid with boundaries, Physics of Fluids, vol.13, issue.11, p.3452, 2001.

X. He and G. Doolen, Lattice Boltzmann Method on Curvilinear Coordinates System : Flow around a Circular Cylinder, Journal of Computational Physics, vol.134, issue.2, pp.306-315, 1997.

C. S. Peskin, The immersed boundary method, Acta Numerica, vol.11, pp.479-517, 2002.

D. R. Noble and J. R. Torczynski, A Lattice-Boltzmann Method for Partially Saturated Computational Cells, International Journal of Modern Physics C, vol.09, issue.08, pp.1189-1201, 1998.

D. R. Owen, C. R. Leonardi, and Y. T. Feng, An efficient framework for fluid-structure interaction using the lattice boltzmann method and immersed moving boundaries, International Journal for Numerical Methods in Engineering, vol.87, issue.1-5, pp.66-95, 2011.

O. , E. Strack, and B. K. Cook, Three-dimensional immersed boundary conditions for moving solids in the lattice-boltzmann method, International Journal for Numerical Methods in Fluids, vol.55, issue.2, pp.103-125, 2007.

O. Malaspinas and P. Sagaut, Advanced large-eddy simulation for lattice Boltzmann methods : The approximate deconvolution model, Physics of Fluids, vol.23, issue.10, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01298910

L. Chen, Q. Kang, Y. Mu, Y. He, and W. Tao, A critical review of the pseudopotential multiphase lattice Boltzmann model : Methods and applications, International Journal of Heat and Mass Transfer, vol.76, pp.210-236, 2014.

D. Lycett, -. Brown, and K. H. Luo, Improved forcing scheme in pseudopotential lattice Boltzmann methods for multiphase flow at arbitrarily high density ratios, Physical Review E -Statistical, Nonlinear, and Soft Matter Physics, vol.91, issue.2, 2015.

X. He, S. Chen, and R. Zhang, A Lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh -Taylor instability, Journal of Computational Physics, vol.663, issue.2, pp.642-663, 1999.

M. Swift, W. Orlandini, J. Osborn, and . Yeomans, Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Physical Review E, vol.54, issue.5, pp.5041-5052, 1996.

U. Ghia, K. N. Ghia, and C. T. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of Computational Physics, vol.48, issue.3, pp.387-411, 1982.

G. Davis, Natural convection of air in a square cavity : A bench mark numerical solution, International Journal for Numerical Methods in Fluids, vol.3, issue.3, pp.249-264, 1983.

P. and L. Quéré, Accurate solutions to the square thermally driven cavity at high Rayleigh number, Computers and Fluids, vol.20, issue.1, pp.29-41, 1991.

T. L. Bo-nan-jiang, L. A. Lin, and . Povinelli, Large-scale computation of incompressible viscous flow by least-squares finite element method, Computer Methods in Applied Mechanics and Engineering, vol.114, issue.3-4, pp.213-231, 1994.

M. Schäfer, S. Turek, F. Durst, E. Krause, and R. Rannacher, Benchmark Computations of Laminar Flow Around a Cylinder, pp.547-566, 1996.

J. C. Anthony and . Ladd, Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part II. Numerical Results, Journal of Fluid Mechanics, vol.271, pp.285-309, 1994.

R. Mei, D. Yu, W. Shyy, and L. Luo, Force evaluation in the lattice boltzmann method involving curved geometry, Phys. Rev. E, vol.65, p.41203, 2002.

D. Makhija, G. Pingen, R. Yang, and K. Maute, Topology optimization of multi-component flows using a multi-relaxation time lattice Boltzmann method, Computers and Fluids, vol.67, pp.104-114, 2012.

E. Rasmus, O. Christiansen, E. Sigmund, and . Fernandez-grande, Experimental validation of a topology optimized acoustic cavity, The Journal of the Acoustical Society of America, vol.138, issue.6, pp.3470-3474, 2015.

H. Mandy-axelle-philippine, O. Zareie, G. M. Sigmund, T. W. Rebeiz, and . Kenny, Experimental validation of topology optimization for rf mems capacitive switch design, Journal of Microelectromechanical Systems, vol.22, issue.6, pp.1296-1309, 2013.

Z. Guo, B. Shi, and N. Wang, Lattice BGK Model for Incompressible Navier-Stokes Equation, Journal of Computational Physics, vol.165, pp.288-306, 2000.

J. Li, Appendix : Chapman-Enskog Expansion in the Lattice Boltzmann Method, p.202, 2015.

. Bibliographie,

S. Cook and . Programming, , 2013.

C. Obrecht, F. Kuznik, B. Tourancheau, and J. J. Roux, Multi-GPU implementation of the lattice Boltzmann method, Computers and Mathematics with Applications, vol.65, issue.2, pp.252-261, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00731106

J. Mark, A. J. Mawson, and . Revell, Memory transfer optimization for a lattice Boltzmann solver on Kepler architecture nVidia GPUs, Computer Physics Communications, vol.185, issue.10, pp.2566-2574, 2014.