On the self-averaging of dispersion for transport in quasi-periodic random media

Nicolae Suciu
(original), ISI/JCR, Numerical Modeling, paper

Abstract

In this study we present a numerical analysis for the self-averaging of the longitudinal dispersion coefficient for transport in heterogeneous media. This is done by investigating the mean-square sample-to-sample fluctuations of the dispersion for finite times and finite numbers of modes for a random field using analytical arguments as well as numerical simulations. We consider transport of point-like injections in a quasi-periodic random field with a Gaussian correlation function. In particular, we focus on the asymptotic and pre-asymptotic behaviour of the fluctuations with the aid of a probability density function for the dispersion, and we verify the logarithmic growth of the sample-to-sample fluctuations as earlier reported in Eberhard (2004 J. Phys. A: Math. Gen. 37 2549–71). We also comment on the choice of the relevant parameters to generate quasi-periodic realizations with respect to the self-averaging of transport in statistically homogeneous Gaussian velocity fields.

Authors

J.P. Eberhard
Simulation in Technology, University of Heidelberg, Germany

N. Suciu
Institute of Applied Mathematics, University of Erlangen-Nuremberg, Germany

C. Vamoş
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords

Cite this paper as

J. Eberhard, N. Suciu, C. Vamoş (2007), On the self-averaging of dispersion for transport in quasi-periodic random media, J. Phys. A: Math. Theor., 40, 597-610, doi: 10.1088/1751-8113/40/4/002

References

see the expanding block below

PDF

https://s3.amazonaws.com/academia.edu.documents/45710946/JPhysA.pdf?AWSAccessKeyId=AKIAIWOWYYGZ2Y53UL3A&Expires=1534852187&Signature=vALZw%2BY8467uCT5ULwJRQ%2Fx%2FLqY%3D&response-content-disposition=inline%3B%20filename%3DOn_the_self-averaging_of_dispersion_for.pdf

soon

About this paper

Cite this paper as:
Eberhard, J., N. Suciu, and, C. Vamoş (2007), On the self-averaging of dispersion for transport in quasi-periodic random media, J. Phys. A: Math. Theor., 40, 597-610, doi:10.1088/1751-8113/40/4/002
Journal

J. Phys. A: Math. Theor.

Publisher Name
DOI

10.1088/1751-8113/40/4/002

Print ISSN

Not available yet.

Online ISSN

Not available yet.

Google Scholar Profile

google scholar profile

[1] M. Clincy and H. Kinzelbach. Stratified disordered media: exact solutions for transport parameters and their self-averaging properties. J. Phys. A: Math. Gen., 34:7141–7152, 2001.
CrossRef (DOI)

[2] G. Dagan. Theory of solute transport by groundwater. Water Resour. Res., 19:183–215, 1987.
CrossRef (DOI)

[3] G. Dagan. Flow and Transport in Porous Formations. Springer Verlag, Berlin, 1989.
CrossRef (DOI)

[4] 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 Resour. Res., 36(12):3591–3604, 2000.
CrossRef (DOI)

[5] M. Dentz, H. Kinzelbach, S. Attinger, and W. Kinzelbach. Temporal behavior of a solute cloud in a heterogeneous porous medium 3. Numerical simulations. Water Resour. Res.,
38(7):23.1–23.13, 2002.
CrossRef (DOI)

[6] M. Dentz, H. Kinzelbach, S. Attinger, and W. Kinzelbach. Numerical studies of the transport behavior of a passive solute in a two-dimensional incompressible random flow field. Phys.
Rev. E, 67(046306):1–10, 2003.
CrossRef (DOI)

[7] J. Eberhard. Approximations for transport parameters and self-averaging properties for pointlike injections in heterogeneous media. J. Phys. A: Math. Gen, 37:2549–2571, 2004.
CrossRef (DOI)

[8] C. W. Gardiner. Handbook of Stochastic Methods (for Physics, Chemistry and Natural Science). Springer, New York, 1985.
CrossRef (DOI)

[9] L. W. Gelhar. Stochastic Subsurface Hydrology. Prentice Hall, New Jersery, 1993.

[10] E. Guyon, C. D. Mitescu, J. Hulin, and S. Roux. Fractals and percolution in porous media and flows? Physica D, 38:172–178, 1989.

[11] U. Jaekel and H. Vereecken. Renormalization group analysis of macrodispersion in a directed random flow. Water Resour. Res., 33(10):2287–2299, 1997.
CrossRef (DOI)

[12] I. Jankovic, A. Fiori, and G. Dagan. Flow and transport in highly heterogeneous formations: 3. Numerical simulations and comparison with theoretical results. Water Resour. Res., 39(9):16.1–16.13, 2003.
CrossRef (DOI)

[13] H. Kesten and G. C. Papanicolaou. A limit theorem for turbulent diffusion. Commun. Math. Phys., 65:97–128, 1979.
CrossRef (DOI)

[14] R. Lenormand and C. Zarcone. Invasion percolation in an etched network: measurement of a fractal dimension. Physical Review Letters, 54(20):2226–2229, 1985.
CrossRef (DOI)

[15] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C: the art of scientific computing. Cambridge University Press, Cambridge, UK, 1992.

[16] H. Schwarze, U. Jaekel, and H. Vereecken. Estimation of macrodispersion by different approximation methods for flow and transport in randomly heterogeneous media. Transport
in Porous Media, 43(2):265–287, 2001.

[17] N. Suciu, C. Vamos,  and J. Eberhard. Evaluation of the first-order approximations for transport in heterogeneous media. Water Resour. Res., 2006.
CrossRef (DOI) (in press).

[18] N. Suciu, C. Vamo¸s, J. Vanderborght, H. Hardelauf, and H. Vereecken. Numerical investigations on ergodicity of solute transport in heterogeneous aquifers. Water Resour. Res., 2006. 42,W04409,
CrossRef (DOI)

[19] M. G. Trefry, F. P. Ruan, and D. McLaughlin. Numerical simulations of preasymptotic transport in heterogeneous porous media: Departures from the Gaussian limit. Water Resour. Res., 39(3):10:1–12, 2003.
CrossRef (DOI)

[20] N. G. van Kampen. Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam, 1981.

[21] C. L. Winter, C. M. Newman, and S. P. Neuman. A perturbation expansion for diffusion in random velocity field. SIAM J. Appl. Math., 44(2):411–424, 1984.
CrossRef (DOI)

soon

2007

Related Posts