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Stochastic Hydrology and Hydraulics

, Volume 11, Issue 6, pp 449–457 | Cite as

A stochastic approach to model bottom boundary conditions and compute efficiency in a settling tank

  • J. Ph. Chancelier
  • M. Cohen de Lara
  • F. Pacard
Originals

Abstract

When the diffusion term is supposed not to be zero at the boundary of a settling tank, we show that an alternate (and equivalent) description to the basic advection-diffusion equation for the concentration of micro pollutant consists in modelling the micro pollutant particles' trajectories as a diffusion stochastic process. Indeed, the density of this latter satisfies the same Pde as the advection-diffusion equation. Our emphasis here is on the computation of the so called tank efficiency and on the bottom boundary conditions. We claim that our interpretation in terms of a diffusion process helps to enlighten the choice of the appropriate mathematical boundary conditions. What is more, we introduce a scouring parameter and give its range as well as its physical interpretation.

Key words

Settling tank diffusion in open sets elastic reflection boundary conditions efficiency exit time 

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References

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • J. Ph. Chancelier
    • 1
  • M. Cohen de Lara
    • 1
  • F. Pacard
    • 1
  1. 1.Cergrene, ENPCMarne la Valleé Cedex 2France

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