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Mathematical Geology

, Volume 28, Issue 1, pp 45–71 | Cite as

Transport in a 2-D saturated porous medium: A new method for particle tracking

  • Frédérick Delay
  • Hélène Housset-Resche
  • Gilles Porel
  • Ghislain de Marsily
Article

Abstract

A new method for solving the transport equation based on the management of a large numbe of particles in a discretized 2-D domain is presented. The method uses numerical variables to represent the number of particles in a given mesh and is more complex than the 1-D problem. The first part of the paper focuses on the specific management of particles in a 2-D problem. The method also would be valid for three dimensions as long as the medium can be modeled similar to a layered system. As the particles are no longer tracked individually, the algorithm is fast and does not depend on the number of particles present. The numerical tests show that the method is nearly numerical dispersion free and permits accurate calculations even for simulations of low-concentration transport. Because each mesh is considered as a closed system between two successive time steps, it is easy to add adsorption phenomenon without any problem of numerical stability. The model is tested under conditions that are extremely demanding for its operating mode and gives a good fit to analytical solutions. The conditions in which it can be used to best advantage are discussed.

Key words

mass transport 2-D advection-dispersion adsorption particle tracking 

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Copyright information

© International Association for Mathematical Geology 1996

Authors and Affiliations

  • Frédérick Delay
    • 1
  • Hélène Housset-Resche
    • 1
  • Gilles Porel
    • 2
  • Ghislain de Marsily
    • 1
  1. 1.Laboratoire de Géologie AppliquéeUniversité Paris VIParis, Cedex 05France
  2. 2.Laboratoire HydrogéologieUniversité de PoitiersPoitiersFrance

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