A stochastic approach to model bottom boundary conditions and compute efficiency in a settling tank
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 wordsSettling tank diffusion in open sets elastic reflection boundary conditions efficiency exit time
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