H. Abdi, The eigen-decomposition: Eigenvalues and eigenvectors, Encyclopedia of Measurement and Statistics, pp.304-308, 2007.

J. Anderson, Computational Fluid Dynamics: The Basics with Applications, 1995.

P. D. Joao, A. M. Angeli, . Valli, C. Neyval, A. F. Reis-jr et al., Finite difference simulations of the Navier-Stokes equations using parallel distributed computing, 15th Symposium on Computer Architecture and High Performance Computing, 2003.

U. M. Ascher and L. R. Petzold, Computational Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, 1998.

K. Atkinson and W. Han, Elementary Numerical Analysis, 2003.

A. Dario, B. Bini, and . Meini, The cyclic reduction algorithm: From Poisson equation to stochastic processes and beyond, Journal of Numerical Algorithm, vol.51, issue.1, pp.23-60, 2009.

D. L. Brown, R. Cortez, and M. L. Minion, Accurate Projection Methods for the Incompressible Navier???Stokes Equations, Journal of Computational Physics, vol.168, issue.2, pp.464-499, 2001.
DOI : 10.1006/jcph.2001.6715

A. Q. Canuto, M. Meneguzzi, and T. Zang, Spectral Methods, 2006.
DOI : 10.1002/0470091355.ecm003m
URL : https://hal.archives-ouvertes.fr/hal-01296839

A. J. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation, vol.22, issue.104, pp.745-762, 1968.
DOI : 10.1090/S0025-5718-1968-0242392-2

G. Cottet and P. Koumoutsakos, Vortex Methods Theory and Practice, 2000.

P. Esterie, M. Gaunard, J. Falcou, J. Lapresté, and B. Rozoy, Boost.simd: generic programming for portable simdization, Proceedings of the 21st international conference on Parallel architectures and compilation techniques, pp.431-432, 2012.

A. Graham, Kronecker Products and Matrix Calculus with Application, 1981.

J. L. Guermond, P. D. Minev, and J. Shen, An overview of projection methods for incompressible flows, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.44-47, pp.6011-6045, 2006.
DOI : 10.1016/j.cma.2005.10.010

F. Harlow and J. E. Welch, Numerical calculation of time-deendent viscous incompressible flow of fluid with free surface. The Physics of Fluids, pp.2182-2189, 1965.

W. Hundsdorfer, Partially Implicit BDF2 Blends for Convection Dominated Flows, SIAM Journal on Numerical Analysis, vol.38, issue.6, pp.1763-1783, 2001.
DOI : 10.1137/S0036142999364741

. Intel, Math Kernel Library (MKL) http://www.intel.com/software/products

G. E. , K. , R. M. Kirby, and I. , Parallel Scientific Computing in C++ and MPI, 2003.

J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations, Journal of Computational Physics, vol.59, issue.2, pp.308-323, 1985.
DOI : 10.1016/0021-9991(85)90148-2

R. J. Leveque, Numerical Methods for Conservation Laws, Lectures in Mathematics. Eth Zurich, 1999.

S. Li and W. Liu, Meshfree and particle methods and their applications, Applied Mechanics Reviews, vol.55, issue.1, pp.1-34, 2002.
DOI : 10.1115/1.1431547
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.9972

D. Martin, P. Colella, N. Keen, A. Deane, G. Brenner et al., An Incompressible Navier-Stokes with Particles Algorithm and Parallel Implementation, Proceedings of the 2005 International Conference on Parallel Computational Fluid Dynamics, pp.461-468, 2006.
DOI : 10.1016/B978-044452206-1/50056-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.392.7383

J. J. Monaghan, Smoothed Particle Hydrodynamics, Annual Review of Astronomy and Astrophysics, vol.30, issue.1, pp.543-574, 1992.
DOI : 10.1146/annurev.aa.30.090192.002551

S. Noury, S. Boivin, and O. L. Maître, A Fast Poisson Solver for OpenCL using Multigrid Methods, GPU Pro2: Advanced Rendering Techniques, 2011.
DOI : 10.1201/b11325-36

O. Pironneau, The Finite Element Method for Fluids, 1990.

E. Polizzi and A. H. Sameh, A parallel hybrid banded system solver: the SPIKE algorithm, Parallel Computing, vol.32, issue.2, pp.177-194, 2006.
DOI : 10.1016/j.parco.2005.07.005

R. Rannacher, Finite element methods for the incompressible Navier-Stokes equations. Fundamental Directions in Mathematical Fluid Mechanics, pp.191-293, 2000.

Y. Saad, Iterative Methods for Sparse Linear Systems. SIAM, 2 edition, 2003.

A. Vincent and M. Meneguzzi, The satial structure and statistical properties of homogeneous turbulence, Journal of Fluid Mechanics, vol.3, issue.-1, pp.1-20, 1991.
DOI : 10.1063/1.863407