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A Lagrangian Stochastic Model for the Transport in Statistically Homogeneous Porous Media

Author

Listed:
  • Kurbanmuradov O.

    (1. Center for Phys. Math. Research, Turkmenian State University, Turkmenbashy av. 31, 744000 Ashgabad, Turkmenistan)

  • Sabelfeld K.

    (2. Institute of Comput. Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentieva str., 6, 630090 Novosibirsk, Russia)

  • Smidts O.F.

    (4. Université Libre de Bruxelles, 50 av. F.D. Roosevelt, B-1050 Brussels - Belgium)

  • Vereecken H.

    (5. Institute of Chemistry and Dynamics of the Geosphere, ICG IV, Agrosphere, Forschungszentrum Jülich, D-52425 Jülich - Germany)

Abstract

A new type of stochastic simulation models is developed for solving transport problems in saturated porous media which is based on a generalized Langevin stochastic differential equation. A detailed derivation of the model is presented in the case when the hydraulic conductivity is assumed to be a random field with a lognormal distribution, being statistically isotropic in space. To construct a model consistent with this statistical information, we use the well-mixed condition which relates the structure of the Langevin equation and the probability density function of the Eulerian velocity field. Numerical simulations of various statistical characteristics like the mean displacement, the displacement covariance tensor and the Lagrangian correlation function are presented. These results are compared against the conventional Direct Simulation Method.

Suggested Citation

  • Kurbanmuradov O. & Sabelfeld K. & Smidts O.F. & Vereecken H., 2003. "A Lagrangian Stochastic Model for the Transport in Statistically Homogeneous Porous Media," Monte Carlo Methods and Applications, De Gruyter, vol. 9(4), pages 341-366, December.
    • Handle: RePEc:bpj:mcmeap:v:9:y:2003:i:4:p:341-366:n:4
    DOI: 10.1515/156939603322601969
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    Citations

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    Cited by:

    1. Shalimova Irina & Sabelfeld Karl K., 2019. "A random walk on small spheres method for solving transient anisotropic diffusion problems," Monte Carlo Methods and Applications, De Gruyter, vol. 25(3), pages 271-282, September.
    2. Kurbanmuradov O. & Sabelfeld K., 2006. "Stochastic Spectral and Fourier-Wavelet Methods for Vector Gaussian Random Fields," Monte Carlo Methods and Applications, De Gruyter, vol. 12(5), pages 395-445, November.
    3. Kolyukhin Dmitry & Sabelfeld Karl, 2005. "Stochastic flow simulation in 3D porous media," Monte Carlo Methods and Applications, De Gruyter, vol. 11(1), pages 15-37, March.
    4. Sabelfeld K. & Kurbanmuradov O. & Levykin A., 2009. "Stochastic simulation of particle transport by a random Darcy flow through a porous cylinder," Monte Carlo Methods and Applications, De Gruyter, vol. 15(1), pages 63-90, January.

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