Global Random Walk Solutions for Flow and Transport in Porous Media

Nicolae Suciu
book chapter, global random walk, Monte Carlo simulations, Numerical Modeling, PDEs

Abstract

This article presents a new approach to solve the equations of flow in heterogeneous porous media by using random walks on regular lattices. The hydraulic head is represented by computational particles which are spread globally from the lattice sites according to random walk rules, with jump probabilities determined by the hydraulic conductivity. The latter is modeled as a realization of a random function generated as a superposition of periodic random modes. One- and two-dimensional numerical solutions are validated by comparisons with analytical manufactured solutions. Further, an ensemble of divergence-free velocity fields computed with the new approach is used to conduct Monte Carlo simulations of diffusion in random fields. The transport equation is solved by a global random walk algorithm which moves computational particles representing the concentration of the solute on the same lattice as that used to solve the flow equations. The integrated flow and transport solution is validated by a good agreement between the statistical estimations of the first two spatial moments of the solute plume and the predictions of the stochastic theory of transport in groundwater.

Authors

Nicolae Suciu, Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords

global random walk; flow in heterogeneous porous media; Monte Carlo simulations.

References

[1] Dagan, G., Flow and Transport in Porous Formations. Springer, Berlin (1989) https://doi.org/10.1007/978-3-642-75015-1
[2] Radu, F.A., Suciu, N., Hoffmann, J., Vogel, A., Kolditz, O., Park, C-H., Attinger, S.: Accuracy of numerical simulations of contaminant transport in heterogeneous aquifers: a comparative study. Adv. Water Resour. 34, 47–61 (2011) http://dx.doi.org/10.1016/j.advwatres.2010.09.012CrossRefGoogle Scholar
[3] Roache, P.J., Code verification by the method of manufactured solutions. J. Fluids Eng. 124 (1):4–10 (2002) http://dx.doi.org/10.1115/1.1436090CrossRefGoogle Scholar
[4] Suciu, N., Diffusion in random velocity fields with applications to contaminant transport in groundwater. Adv. Water Resour. 69 (2014) 114-133. http://dx.doi.org/10.1016/j.advwatres.2014.04.002CrossRefGoogle Scholar
[5] Suciu, N., Diffusion in Random Fields. Applications to Transport in Groundwater. Birkhäuser, Cham (2019) https://doi.org/10.1007/978-3-030-15081-5
[6] Suciu, N., Vamoş, C.: Evaluation of overshooting errors in particle methods for diffusion by biased global random walk. Rev. Anal. Num. Th. Approx. (Romanian Academy) 35, 119–126 (2006) https://ictp.acad.ro/jnaat/journal/article/view/2006-vol35-no1-art17
[7] Vamoş, C., Suciu, N., Vereecken, H.: Generalized random walk algorithm for the numerical modeling of complex diffusion processes. J. Comput. Phys., 186, 527–544 (2003) https://doi.org/10.1016/S0021-9991(03)00073-1.MathSciNetCrossRefGoogle Scholar

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https://link.springer.com/content/pdf/10.1007%2F978-3-030-55874-1_93.pdf

Cite this paper as:

N. Suciu, Global Random Walk Solutions for Flow and Transport in Porous Media, in: F.J. Vermolen, C. Vuik (eds.), Numerical Mathematics and Advanced Applications ENUMATH 2019, Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham, pp. 939-947, doi: https://doi.org/10.1007/978-3-030-55874-1_93

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Journal

Springer

Publisher Name

Numerical Mathematics and Advanced Applications ENUMATH

DOI

http://doi.org/10.1007/978-3-030-55874-1_93

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