Ergodic simulations of diffusion in random velocity fields

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

Abstract

Ergodic simulations aim at estimating ensemble average characteristics of diffusion in random fields from space averages. The traditional approach, based on large supports of the initial concentration in general fails to obtain ergodic simulations.
However, such simulations, using single realizations of the velocity, are shown to be feasible if space averages with respect to the location of the initial concentration support are used to estimate ensemble averages.

Authors

N. Suciu
Friedrich-Alexander University of Erlangen-Nuremberg,
Institute of Applied Mathematics, Martensstrasse 3, 91058 Erlangen, Germany

C. Vamos
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy,  Cluj-Napoca, Romania

K. Sabelfeld
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany, and
Institute of Computational Mathematics and Mathem. Geophysics, Russian Acad. Sci., Lavrentieva str., 6, Novosibirsk, Russia

Keywords

Point Source; Space Average; Ensemble Average; Large Source; Transport Simulation.

References

See the expanding block below.

Chapter coordinates

N. Suciu, C. Vamoş and K. Sabelfeld, Ergodic simulations of diffusion in random velocity fields, in Monte Carlo and Quasi-Monte Carlo Methods 2006, Ed. A. Keller, S. Heinrich, and H. Niederreiter, Springer Verlag, Heidelberg, 2008 pp. 659-668
doi: 10.1007/978-3-540-74496-2_40, ISBN: 978-3-540-74495-5.

PDF

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.528.2624&rep=rep1&type=pdf

http://dx.doi.org/doi:10.1007/978-3-540-74496-2_40

About this chapter

Book title

Monte Carlo and Quasi-Monte Carlo Methods

Publisher Name

Springer Verlag, Heidelberg

DOI

10.1007/978-3-540-74496-2_40 

Print ISSN

978-3-540-74496-2

Online ISSN

978-3-540-74495-5

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[CD99] J. P. Chiles and P. Delfiner. Geostatisctics: Modeling Spatial Uncertainty. Wiley, New York (1999)

[KKS05] P. Kramer, O. Kurbanmuradov, and K. Sabelfeld. Extension of multiscale Gaussian random field simulations algorithm. Weierstrass Institute, Berlin, Preprint 1040 (2005)

[MM80] G. Matheron and G. de Marsily. Is transport in porous media always diffusive? Water Resour. Res., 16, 901–917 (1980)

[MPS93] J. Misguish, G. Pelletier, and P. Schuck (editors). Statistical Description of Transport in Plasma, Astra- and Nuclear Physics. Les Houches Series, Nova Science Publ., Inc., New York (1993)

[MY75] A. S. Monin and A. M. Yaglom. Statistical Fluid Mechanics: Mechanics of Turbulence. MIT Press, Cambridge, M A (1975)

[SVV04] N. Suciu, C. Vamos, J. Vanderborght, H. Hardelauf, and H. Vereecken. Numerical modeling of large scale transport of contaminant solutes using the global random walk algorithm. Monte Carlo Methods and Appl., 10(2), 153–177 (2004)

[SV06] N. Suciu and C. Vamos. Evaluation of overshooting errors in particle methods for diffusion by biased global random walk. Rev. Anal. Num. Th. Approx., 35, 119-126 (2006)

[SVV06] 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., 42, W04409, doi:10.1029/2005WR004546 (2006)

[SVE06] N. Suciu, C. Vamos, and J. Eberhard. Evaluation of the first-order approximations for transport in heterogeneous media. Water Resour. Res., 42, W11504, doi: 10.1029/2005WR004714 (2006)

[SVV07] N. Suciu, C. Vamo¸s, and H. Vereecken. Multiple meanings of ergodicity in real life problems. In: Marinoschi, G., Ion, S., Popa, C. (ed) Proceedings of the 5th Workshop on Mathematical Modelling of Environmental and Life Sciences Problems. Rom. Acad. Publishing House, Bucharest (2007, to appear)

[VSV03] C. Vamos, N. Suciu, and H. Vereecken. Generalized random walk algorithm for the numerical modeling of complex diffusion processes, J. Comp. Phys., 186(2), 527–544 (2003)

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