R. Ababou, Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media, Transp. Porous Media, pp.549-565, 1989.

P. Ackerer and W. Kinzelbach, Modélisation du transport de contaminant par la méthode de marche au hasard: Influence des variations du champ d'e ´coulement au cours du temps sur la dispersion, paper presented at Approach to Subsurface Flow, Int. Assoc. Hydraul. Res, 1985.

F. Alabert, The practice of fast conditional simulations through the LU decomposition of the covariance matrix, Mathematical Geology, vol.19, issue.2, pp.369-386, 1987.
DOI : 10.1007/BF00897191

A. Beaudoin, An Efficient Parallel Particle Tracker for Advection-Diffusion Simulations in Heterogeneous Porous Media, Europar, pp.705-714, 2007.
DOI : 10.1007/978-3-540-74466-5_76

URL : https://hal.archives-ouvertes.fr/insu-00260740

A. Beaudoin, J. De-dreuzy, and J. Erhel, Numerical Monte Carlo analysis of the influence of pore-scale dispersion on macrodispersion in 2-D heterogeneous porous media, Water Resources Research, vol.146, issue.3, pp.10-1029, 2010.
DOI : 10.1029/2010WR009576

URL : https://hal.archives-ouvertes.fr/insu-00610159

A. Bellin, P. Salandin, and A. Rinaldo, Simulation of dispersion in heterogeneous porous formations: Statistics, first-order theories, convergence of computations, Water Resources Research, vol.26, issue.5, pp.2211-222710, 1992.
DOI : 10.1029/92WR00578

G. Chavent and J. E. Roberts, A unified physical presentation of mixed, mixed-hybrid finite elements and standard finite difference approximations for the determination of velocities in waterflow problems, Advances in Water Resources, vol.14, issue.6, pp.329-348, 1991.
DOI : 10.1016/0309-1708(91)90020-O

O. A. Cirpka and S. Attinger, Effective dispersion in heterogeneous media under random transient flow conditions, Water Resources Research, vol.36, issue.9, pp.125710-1029, 2003.
DOI : 10.1029/2002WR001931

G. Dagan, Solute transport in heterogeneous porous formations, Journal of Fluid Mechanics, vol.18, issue.-1, pp.151-177, 1984.
DOI : 10.1017/S0022112075000213

G. Dagan, Flow and Transport in Porous Formations, 1989.
DOI : 10.1007/978-3-642-75015-1

G. Dagan, A. Bellin, and Y. Rubin, Lagrangian Analysis of Transport in Heterogeneous Formations Under Transient Flow Conditions, Water Resources Research, vol.26, issue.4, pp.891-89910, 1996.
DOI : 10.1029/95WR02497

M. W. Davis, Production of conditional simulations via the LU triangular decomposition of the covariance matrix, Math. Geol, vol.19, issue.2, pp.91-98, 1987.

J. De-dreuzy, A. Beaudoin, and J. Erhel, Asymptotic dispersion in 2D heterogeneous porous media determined by parallel numerical simulations, Water Resources Research, vol.36, issue.3, pp.10-1029, 2007.
DOI : 10.1029/2006WR005394

URL : https://hal.archives-ouvertes.fr/insu-00193397

F. Delay, Simulating Solute Transport in Porous or Fractured Formations Using Random Walk Particle Tracking, Vadose Zone Journal, vol.4, issue.2, pp.360-379, 2005.
DOI : 10.2136/vzj2004.0125

M. Dentz and J. Carrera, Effective dispersion in temporally fluctuating flow through a heterogeneous medium, Physical Review E, vol.68, issue.3, 2003.
DOI : 10.1103/PhysRevE.68.036310

URL : https://hal.archives-ouvertes.fr/insu-00620769

M. Dentz and J. Carrera, Effective solute transport in temporally fluctuating flow through heterogeneous media, Water Resources Research, vol.32, issue.4, pp.10-1029, 2005.
DOI : 10.1029/2004WR003571

M. Dentz, H. Kinzelbach, S. Attinger, and W. Kinzelbach, Temporal behavior of a solute cloud in a heterogeneous porous medium: 1. Point-like injection, Water Resources Research, vol.2, issue.12, pp.3591-360410, 2000.
DOI : 10.1029/2000WR900162

M. Dentz, Erratum: Effective dispersion in temporally fluctuating flow through a heterogeneous medium, Phys. Rev. E, vol.84, 2011.
URL : https://hal.archives-ouvertes.fr/insu-00620769

A. Englert, J. Vanderborght, and H. Vereecken, Prediction of velocity statistics in three-dimensional multi-Gaussian hydraulic conductivity fields, Water Resources Research, vol.45, issue.10, pp.10-1029, 2006.
DOI : 10.1029/2002WR001721

J. Erhel, A parallel scientific software for heterogeneous hydrogeoloy, in Parallel Computational Fluid Dynamics, pp.39-48, 2007.

R. D. Falgout, 's conceptual interfaces, ACM Transactions on Mathematical Software, vol.31, issue.3, pp.31-326, 2005.
DOI : 10.1145/1089014.1089018

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

A. D. Festger and G. R. Walter, The Capture Efficiency Map: The Capture Zone Under Time-Varying Flow, Ground Water, vol.15, issue.4, pp.619-628, 2002.
DOI : 10.1111/j.1745-6584.1997.tb00152.x

M. Frigo and S. G. Johnson, The Design and Implementation of FFTW3, Proc. IEEE, pp.216-231, 2005.
DOI : 10.1109/JPROC.2004.840301

L. W. Gelhar and C. L. Axness, Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resources Research, vol.104, issue.4, pp.161-180, 1983.
DOI : 10.1029/WR019i001p00161

L. W. Gelhar, C. Welty, and K. R. Rehfeldt, A critical review of data on field-scale dispersion in aquifers, Water Resources Research, vol.16, issue.6, pp.1955-197410, 1992.
DOI : 10.1029/92WR00607

D. J. Goode and L. F. Konikow, Apparent dispersion in transient groundwater flow, Water Resources Research, vol.41, issue.6, pp.2339-2351, 1990.
DOI : 10.1029/WR026i010p02339

A. L. Gutjahr, Fast Fourier transforms for random field generation, New Mexico Inst. of Mining and Tech, 1989.

W. Kinzelbach, The random-walk method in pollutant transport simulation, in Groundwater Flow and Quality Modelling, NATO ASI Ser. C, vol.224, pp.227-246, 1988.

W. Kinzelbach and P. Ackerer, Modélisation de la propagation d'un contaminant dans un champ d'e ´coulement transitoire, pp.197-206, 1986.

P. K. Kitanidis, Prediction by the method of moments of transport in a heterogeneous formation, Journal of Hydrology, vol.102, issue.1-4, pp.1-4, 1988.
DOI : 10.1016/0022-1694(88)90111-4

L. Borgne and T. , Non-Fickian mixing: Temporal evolution of the scalar dissipation rate in heterogeneous porous media, Advances in Water Resources, vol.33, issue.12, pp.1468-1475, 2010.
DOI : 10.1016/j.advwatres.2010.08.006

URL : https://hal.archives-ouvertes.fr/insu-00610129

L. Borgne and T. , Persistence of incomplete mixing: A key to anomalous transport, Physical Review E, vol.84, issue.1, 2011.
DOI : 10.1103/PhysRevE.84.015301

URL : https://hal.archives-ouvertes.fr/insu-00620762

L. Ravalec and M. , The FFT moving average (FFT-MA) generator: An efficient numerical method for generating and conditioning gaussian simulations, Mathematical Geology, vol.32, issue.6, pp.701-723, 2000.
DOI : 10.1023/A:1007542406333

R. L. Naff, T. Yeh, and M. Kemblowski, Reply [to ???Comment on ???A note on the recent natural gradient tracer test at the Borden site??? by R. L. Naff, T.-C. Jim Yeh, and M.W. Kemblowski???], Reply, pp.2523-2525, 1989.
DOI : 10.1029/WR025i012p02523

S. Neuman, C. L. Winter, and C. M. Newman, Stochastic theory of field-scale fickian dispersion in anisotropic porous media, Water Resources Research, vol.44, issue.2, pp.453-466, 1987.
DOI : 10.1029/WR023i003p00453

E. Pardo-iguzquiza and M. Chica-olmo, The Fourier Integral Method: An efficient spectral method for simulation of random fields, Mathematical Geology, vol.25, issue.2, pp.177-217, 1993.
DOI : 10.1007/BF00893272

D. W. Pollock, Semianalytical Computation of Path Lines for Finite-Difference Models, Ground Water, vol.25, issue.3, pp.743-750, 1988.
DOI : 10.1111/j.1745-6584.1988.tb00425.x

J. M. Ramirez, E. A. Thomann, E. C. Waymire, J. Chastanet, and B. D. Wood, A note on the theoretical foundations of particle tracking methods in heterogeneous porous media, Water Resources Research, vol.9, issue.53, pp.10-1029, 2008.
DOI : 10.1029/2007WR005914

K. R. Rehfeldt and L. W. Gelhar, Stochastic analysis of dispersion in unsteady flow in heterogeneous aquifers, Water Resources Research, vol.27, issue.4, pp.2085-2099, 1992.
DOI : 10.1029/92WR00750

P. Salamon, A review and numerical assessment of the random walk particle tracking method, Journal of Contaminant Hydrology, vol.87, issue.3-4, pp.3-4, 2006.
DOI : 10.1016/j.jconhyd.2006.05.005

P. Salandin and V. Fiorotto, Solute transport in highly heterogeneous aquifers, Water Resources Research, vol.26, issue.5, pp.949-961, 1998.
DOI : 10.1029/98WR00219

E. A. Sudicky, A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process, Water Resources Research, vol.44, issue.2, pp.2069-2082, 1986.
DOI : 10.1029/WR022i013p02069

J. F. Sykes, S. B. Pahwa, R. B. Lantz, and D. S. Ward, Numerical simulation of flow and contaminant migration at an extensively monitored landfill, Water Resources Research, vol.8, issue.1, pp.1687-1704, 1982.
DOI : 10.1029/WR018i006p01687

G. Taylor, Dispersion of Soluble Matter in Solvent Flowing Slowly through a Tube, Proc. R. Soc. London Ser. A, pp.219-186, 1137.
DOI : 10.1098/rspa.1953.0139

M. G. Trefry, F. P. Ruan, and D. Mclaughlin, Numerical simulations of preasymptotic transport in heterogeneous porous media: Departures from the Gaussian limit, Water Resources Research, vol.26, issue.10, pp.106310-1029, 2003.
DOI : 10.1029/2001WR001101

X. H. Wen and J. J. Gomez-hernandez, The Constant Displacement Scheme for Tracking Particles in Heterogeneous Aquifers, Ground Water, vol.34, issue.1, pp.135-142, 1996.
DOI : 10.1111/j.1745-6584.1996.tb01873.x

D. X. Zhang and S. P. Neuman, Head and Velocity Covariances Under Quasi-Steady State flow and their Effects on Advective Transport, Water Resources Research, vol.31, issue.12, pp.77-83, 1996.
DOI : 10.1029/95WR02766

J. Carrera, J. De-dreuzy, M. Dentz, and . Ghs, Institute of Environmental Analysis and Water Studies, C/ Jordi Girona 18?26, 08034 Barcelona , Spain. (jean-raynald.de-dreuzy@univ-rennes1.fr) T. Le Borgne, p.35042