]. P. Albuquerque, D. Alemani, B. Chopard, and P. Leone, Coupling a Lattice Boltzmann and a Finite Difference Scheme, Proceedings of ICCS 2004: 4th International Conference on Computational Science, pp.540-547, 2004.
DOI : 10.1007/978-3-540-25944-2_70

A. Ammar, Lattice Boltzmann method for polymer kinetic theory, Journal of Non-Newtonian Fluid Mechanics, vol.165, issue.19-20, pp.1082-1092, 2010.
DOI : 10.1016/j.jnnfm.2010.05.006

J. Kamga and O. Pironneau, Numerical zoom for multiscale problems with an application to nuclear waste disposal, Journal of Computational Physics, vol.224, issue.1, pp.403-413, 2007.
DOI : 10.1016/j.jcp.2007.03.020

M. Astorino, J. Becerra-sagredo, and A. Quarteroni, A modular lattice boltzmann solver for GPU computing processors, SeMA Journal, vol.35, issue.8???9, pp.53-78, 2012.
DOI : 10.1007/BF03322610

L. Baffico, S. Bernard, Y. Maday, G. Turinici, and G. Zérah, Parallel-in-time molecular-dynamics simulations, Physical Review E, vol.66, issue.5, pp.66-057701, 2002.
DOI : 10.1103/PhysRevE.66.057701
URL : https://hal.archives-ouvertes.fr/hal-00536574

M. Bernaschi, M. Fatica, S. Melchionna, S. Succi, and E. Kaxiras, A flexible high-performance lattice Boltzmann GPU code for the simulations of fluid flows in complex geometries, Concurrency-Pract, Ex, vol.22, pp.1-14, 2010.

L. A. Berry, W. Elwasif, J. M. Reynolds-barredo, D. Samaddar, R. Sanchez et al., Event-based parareal: A data-flow based implementation of parareal, Journal of Computational Physics, vol.231, issue.17, pp.231-5945, 2012.
DOI : 10.1016/j.jcp.2012.05.016

A. Blouza, L. Boudin, and S. Kaber, Parallel in time algorithms with reduction methods for solving chemical kinetics, Communications in Applied Mathematics and Computational Science, vol.5, issue.2, pp.241-263, 2010.
DOI : 10.2140/camcos.2010.5.241
URL : https://hal.archives-ouvertes.fr/inria-00541025

A. Caiazzo, Asymptotic Analysis of lattice Boltzmann method for Fluid-Structure Interaction problems, 2007.

A. Caiazzo and M. Junk, Asymptotic Analysis of Lattice Boltzmann Methods for Flow-Rigid Body Interaction, Progress in Computational Physics, p.91, 2013.
DOI : 10.2174/9781608057160113030007

P. Chen, The lattice Boltzmann method for fluid dynamics: theory and applications, Master's thesis, EPFL, 2011.

S. S. Chikatamarla, S. Ansumali, and I. V. Karlin, Grad's approximation for missing data in lattice Boltzmann simulations, Europhysics Letters (EPL), vol.74, issue.2, pp.215-221, 2006.
DOI : 10.1209/epl/i2005-10535-x

B. Chopard, J. L. Falcone, and J. Latt, The lattice Boltzmann advection-diffusion model revisited, The European Physical Journal Special Topics, vol.171, issue.1, pp.245-249, 2009.
DOI : 10.1140/epjst/e2009-01035-5

F. Chouly and A. Lozinski, Parareal multi-model numerical zoom for parabolic multiscale problems, Comptes Rendus Mathematique, vol.352, issue.6, pp.535-540, 2014.
DOI : 10.1016/j.crma.2014.03.018
URL : https://hal.archives-ouvertes.fr/hal-00934390

A. Dervieux, Fluid-structure interaction, 2000.

M. Discacciati and A. Quarteroni, Navier-Stokes/darcy coupling: modeling, analysis, and numerical approximation, Revista Matem??tica Complutense, vol.22, issue.2, pp.315-426, 2009.
DOI : 10.5209/rev_REMA.2009.v22.n2.16263

A. Dupuis, E. Kotsalis, and P. Koumoutsakos, Coupling lattice Boltzmann and molecular dynamics models for dense fluids, Physical Review E, vol.75, issue.4, pp.75-046704, 2007.
DOI : 10.1103/PhysRevE.75.046704

A. Dupuis and P. Koumoutsakos, Effects of atomistic domain size on hybrid lattice Boltzmannmolecular dynamics simulations of dense fluids, Int. J. Mod. Phys. C, pp.18-644, 2007.

S. Engblom, Parallel in Time Simulation of Multiscale Stochastic Chemical Kinetics, Multiscale Modeling & Simulation, vol.8, issue.1, pp.46-68, 2009.
DOI : 10.1137/080733723

A. Ern and J. Guermond, Theory and practice of finite elements, of Applied Mathematical Sciences, 2004.
DOI : 10.1007/978-1-4757-4355-5

C. Farhat and M. Chandesris, Time-decomposed parallel time-integrators: theory and feasibility studies for fluid, structure, and fluid-structure applications, International Journal for Numerical Methods in Engineering, vol.36, issue.9, pp.1397-1434, 2003.
DOI : 10.1002/nme.860

D. Fedosov and G. Karniadakis, Triple-decker: Interfacing atomistic???mesoscopic???continuum flow regimes, Journal of Computational Physics, vol.228, issue.4, pp.1157-1171, 2009.
DOI : 10.1016/j.jcp.2008.10.024

M. A. Fernández, L. Formaggia, J. Gerbeau, and A. Quarteroni, The derivation of the equations for fluids and structure, Cardiovascular mathematics, pp.77-121, 2009.
DOI : 10.1007/978-88-470-1152-6_3

P. Fischer, F. Hecht, and Y. Maday, A parareal in time semi-implicit approximation of the Navier- Stokes equations, Domain decomposition methods in science and engineering, pp.433-440, 2005.

M. Fyta, S. Melchionna, E. Kaxiras, and S. Succi, Multiscale Coupling of Molecular Dynamics and Hydrodynamics: Application to DNA Translocation through a Nanopore, Multiscale Modeling & Simulation, vol.5, issue.4, pp.1156-1173, 2006.
DOI : 10.1137/060660576

M. Gander and S. Vandewalle, Analysis of the Parareal Time???Parallel Time???Integration Method, SIAM Journal on Scientific Computing, vol.29, issue.2, pp.556-578, 2007.
DOI : 10.1137/05064607X

R. Glowinski, J. He, A. Lozinski, J. Rappaz, and J. Wagner, Finite element approximation of multi-scale elliptic problems using patches of elements, Numerische Mathematik, vol.49, issue.4, pp.663-687, 2005.
DOI : 10.1007/s00211-005-0614-5
URL : https://hal.archives-ouvertes.fr/hal-00113130

L. He, The Reduced Basis Technique as a Coarse Solver for Parareal in Time Simulations, Journal of Computational Mathematics, vol.28, pp.676-692, 2010.
DOI : 10.4208/jcm.1003-m2980

F. Hecht, A. Lozinski, and O. Pironneau, Numerical Zoom and the Schwarz Algorithm, Lect. Notes Comput. Sci. Eng, vol.70, pp.63-73, 2009.
DOI : 10.1007/978-3-642-02677-5_6
URL : https://hal.archives-ouvertes.fr/hal-00628622

F. Hecht, O. Pironneau, J. Morice, A. L. Hyaric, and K. Ohtsuka, Freefem++ documentation, 2012.

D. M. Heyes, J. Baxter, U. Tüzün, and R. S. Qin, Discrete-element method simulations: from micro to macro scales, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci, pp.362-1853, 2004.

A. Hiorth, U. H. Lad, S. Evje, and S. M. Skjaeveland, A lattice Boltzmann-BGK algorithm for a diffusion equation with Robin boundary condition-application to NMR relaxation, International Journal for Numerical Methods in Fluids, vol.79, issue.B10, pp.59-405, 2009.
DOI : 10.1016/j.jcp.2006.08.021

H. Huang, X. Lu, and M. Sukop, Numerical study of lattice Boltzmann methods for a convection???diffusion equation coupled with Navier???Stokes equations, Journal of Physics A: Mathematical and Theoretical, vol.44, issue.5, pp.44-055001, 2011.
DOI : 10.1088/1751-8113/44/5/055001

M. Junk, A. Klar, and L. Luo, Asymptotic analysis of the lattice Boltzmann equation, Journal of Computational Physics, vol.210, issue.2, pp.676-704, 2005.
DOI : 10.1016/j.jcp.2005.05.003

P. Kao and R. Yang, An investigation into curved and moving boundary treatments in the lattice Boltzmann method, Journal of Computational Physics, vol.227, issue.11, pp.5671-5690, 2008.
DOI : 10.1016/j.jcp.2008.02.002

P. Ladevèze, J. Passieux, and D. Néron, The LATIN multiscale computational method and the Proper Generalized Decomposition, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.199-1287, 2010.
DOI : 10.1016/j.cma.2009.06.023

J. Lätt, Hydrodynamic limit of lattice Boltzmann equations, 2007.

J. Lätt, B. Chopard, O. Malaspinas, M. Deville, and A. Michler, Straight velocity boundaries in the lattice Boltzmann method, Physical Review E, vol.77, issue.5, pp.77-056703, 2008.
DOI : 10.1103/PhysRevE.77.056703

F. Legoll, T. Lelì, and G. Samaey, A Micro-Macro Parareal Algorithm: Application to Singularly Perturbed Ordinary Differential Equations, SIAM Journal on Scientific Computing, vol.35, issue.4, pp.1951-1986, 2013.
DOI : 10.1137/120872681
URL : https://hal.archives-ouvertes.fr/hal-00691939

J. Lions, Y. Maday, and G. Turinici, R??solution d'EDP par un sch??ma en temps ??parar??el ??, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.7, pp.332-661, 2001.
DOI : 10.1016/S0764-4442(00)01793-6

H. B. Luan, H. Xu, L. Chen, D. L. Sun, and W. Q. Tao, Numerical Illustrations of the Coupling Between the Lattice Boltzmann Method and Finite-Type Macro-Numerical Methods, Numerical Heat Transfer, Part B: Fundamentals, vol.67, issue.2, pp.147-171, 2010.
DOI : 10.1016/0021-9991(82)90058-4

Y. Maday and G. Turinici, The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation, Lect. Notes Comput. Sci. Eng, vol.40, pp.441-448, 2005.
DOI : 10.1007/3-540-26825-1_45
URL : https://hal.archives-ouvertes.fr/hal-00798334

O. Malaspinas, B. Chopard, and J. Latt, General regularized boundary condition for multi-speed lattice Boltzmann models, Computers & Fluids, vol.49, issue.1, pp.49-78, 2011.
DOI : 10.1016/j.compfluid.2011.04.010

R. Mei, L. Luo, and P. , Lallemand, and D. dHumì eres, Consistent initial conditions for lattice Boltzmann simulations, Comput. Fluids, pp.35-855, 2006.

S. Melchionna, M. Fyta, E. Kaxiras, and S. Succi, Exploring DNA translocation trough a nanopore via a multiscale lattice-Boltzmann molecular-dynamics methodology, Int. J. Mod. Phys. C, pp.18-685, 2007.

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, Physical Review E, vol.89, issue.2, pp.89-023303, 2014.
DOI : 10.1103/PhysRevE.89.023303

A. S. Nielsen, Feasibility study of the parareal algorithm, 2012.

K. Perktold, M. Prosi, and P. Zunino, Mathematical models of mass transfer in the vascular walls, Cardiovascular mathematics, pp.243-278, 2009.
DOI : 10.1007/978-88-470-1152-6_7

Y. Qian, D. Humieres, and P. Lallemand, Lattice BGK Models for Navier-Stokes Equation, Europhysics Letters (EPL), vol.17, issue.6, p.479, 1992.
DOI : 10.1209/0295-5075/17/6/001

A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential equations, 1997.

G. Romano, Handshaking multiscale thermal model of nanostructured devices, 2010 14th International Workshop on Computational Electronics, 2010.
DOI : 10.1109/IWCE.2010.5677942

J. Russo, J. Horbach, F. Sciortino, and S. Succi, Nanoflows through disordered media: A joint lattice Boltzmann and molecular dynamics investigation, EPL (Europhysics Letters), vol.89, issue.4, pp.89-44001, 2010.
DOI : 10.1209/0295-5075/89/44001

X. Shan, X. Yuan, and H. Chen, Kinetic theory representation of hydrodynamics: a way beyond the Navier???Stokes equation, Journal of Fluid Mechanics, vol.550, issue.-1, pp.413-441, 2006.
DOI : 10.1017/S0022112005008153

S. Singh, G. Subramanian, and S. Ansumali, Lattice Fokker Planck for dilute polymer dynamics, Physical Review E, vol.88, issue.1, pp.88-013301, 2013.
DOI : 10.1103/PhysRevE.88.013301

A. Srinivasan and N. Chandra, Latency tolerance through parallelization of time in scientific applications, Parallel Computing, vol.31, issue.7, pp.777-796, 2005.
DOI : 10.1016/j.parco.2005.04.008

H. Stetter, The defect correction principle and discretization methods, Numerische Mathematik, vol.11, issue.4, pp.425-443, 1978.
DOI : 10.1007/BF01432879

S. Succi, O. Filippova, G. Smith, and E. Kaxiras, Applying the lattice Boltzmann equation to multiscale fluid problems, Computing in Science & Engineering, vol.3, issue.6, pp.26-37, 2001.
DOI : 10.1109/5992.963425

P. Van-leemput, C. Vandekerckhove, W. Vanroose, and D. Roose, Accuracy of Hybrid Lattice Boltzmann/Finite Difference Schemes for Reaction-Diffusion Systems, Multiscale Modeling & Simulation, vol.6, issue.3, pp.838-857, 2007.
DOI : 10.1137/060675113

Y. Vanderhoydonc and W. Vanroose, Numerical Extraction of a Macroscopic PDE and a Lifting Operator from a Lattice Boltzmann Model, Multiscale Modeling & Simulation, vol.10, issue.3, pp.766-791, 2012.
DOI : 10.1137/110842739

J. C. Verschaeve and B. Müller, A curved no-slip boundary condition for the lattice Boltzmann method, Journal of Computational Physics, vol.229, issue.19, pp.6781-6803, 2010.
DOI : 10.1016/j.jcp.2010.05.022

E. Weinberg, D. Shahmirzadi, and M. Mofrad, On the multiscale modeling of heart valve biomechanics in health and disease, Biomechanics and Modeling in Mechanobiology, vol.32, issue.16, pp.373-387, 2010.
DOI : 10.1007/s10237-009-0181-2

P. Wriggers and M. Hain, Micro-meso-macro modelling of composite materials, III European Conference on Computational Mechanics, pp.37-37, 2006.

H. Xu, H. Luan, Y. He, and W. Tao, A lifting relation from macroscopic variables to mesoscopic variables in lattice Boltzmann method: Derivation, numerical assessments and coupling computations validation, Computers & Fluids, vol.54, pp.54-92, 2012.
DOI : 10.1016/j.compfluid.2011.10.007

D. P. Ziegler, Boundary conditions for lattice Boltzmann simulations, Journal of Statistical Physics, vol.9, issue.5-6, pp.1171-1177, 1993.
DOI : 10.1007/BF01049965