Abstract
A 3D Cellular Automata (CA) model for simulating fluid permeation through porous material with complex morphology is developed and investigated. The model is a composition of two interacting CA: one, simulating fluid convection, induced either by gravitation force or by external pressure, and another — simulating fluid surface leveling by diffusion. Both CA process the same discrete space, their operation being separated in time and space, which simplifies essentially parallel implementation. The CA model is tested on an example of water permeation through soil. Results of its parallel implementation on a multiprocessor with distributed memory are presented. A tomographic digitized representation of a 3D soil sample was kindly given by Prof.Wim Cornelis. The simulation program was implemented on the cluster of Siberian Supercomputer Center of Siberian Branch of Russian Academy of Science.
Supported by (1)Presidium of Russian Academy of Sciences, Basic Research Program 15-9 (2013), (2) Siberian Branch of Russian Academy of Sciences, Interdisciplinary Project 47, (3) Russian Fund for Basic Research grant 11-01-00567a.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bandman, O.: Using cellular automata for porous media simulation. J. of Supercomputing 57(2), 121–131 (2011)
Keller, L.M., et al.: 3D geometry and topology of pore pathways in Opalinus clay: Implications for mass transport. Appl. Clay Science 52, 85–95 (2011)
Rothman, B.H., Zaleski, S.: Lattice-Gas Cellular Automata. Simple Models of Complex Hydrodynamics. Cambridge Univ. Press (1997)
Hidemitsu, H.: Lattice Boltzmann Method and its Application to Flow Analysis in Porous Media. R&D Review of Toyota CRDL 38(1), 17–25 (2007)
Hoekstra, A.G., et al. (eds.): Simulating Complex Systems by Cellular Automata. Understanding complex Systems. Springer, Berlin (2010)
Bandman, O.L.: Cellular-Automata models of Spatial Dynamics Simulation. System Informatics (10), 58–116 (2006) (in Russian)
Frish, U., Hasslacher, B., Pomeau, Y.: Lattice-gas Automata for Navier-Stokes equation. Phys. Rev. Letters 56, 1505–1508 (1986)
Sahimi, M.: Flow phenomena in rocks: from continuum models to fractals, percolation, cellular automata, and simulation annealing. Review in Modern Physics 65(4), 1393–1534 (1993)
Jansen, A.P.J.: An Introduction to Monte-Carlo Simulation of Surface Reactions, arXiv:cond-mat/0303028v1[stat-mech] (2003)
Bandman, O.: Parallel Simulation of Asynchronous Cellular Automata Evolution. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds.) ACRI 2006. LNCS, vol. 4173, pp. 41–47. Springer, Heidelberg (2006)
Achasova, S., Bandman, O.: Correctness of parallel Processes. Nauka, Novosibirsk (1999) (in Russian)
Kalgin, K.: Parallel implementation of asynchronous cellular automama on 32-core computer. Siberian J. Num. Math. 15(1), 55–65 (2012)
Gardner, M.: Mathematical Games - the fantastic combinations of John Conway’s new solitaire game ”life”. Scientific American 223, 120–123 (1970)
Bandman, O.: Cellular Automata Composition Techniques for Spatial Dynamics Simulation. In: Hoekstra, A.G., et al. (eds.) Simulating Complex Systems by Cellular Automata. Understanding complex Systems, pp. 81–115. Springer, Berlin (2010)
Toffolli, T., Margolus, N.: Cellular Automata Machines: A new Environment for Modeling. MIT Press, USA (1987)
Ramirez, A., Jaramillo, D.E.: Porous media generated by using an immiscible Lattice-Gas model. Computational Material Science 65, 157–164 (2012)
Basndman, O.: Invariants of cellular automata reactioon-diffusion models. Applied Discrete Mathematics (3), 55–64 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bandman, O. (2013). 3-D Cellular Automata Model of Fluid Permeation through Porous Material. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2013. Lecture Notes in Computer Science, vol 7979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39958-9_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-39958-9_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39957-2
Online ISBN: 978-3-642-39958-9
eBook Packages: Computer ScienceComputer Science (R0)