A STOCHASTIC APPROACH TO MODEL BOTTOM BOUNDARY-CONDITIONS AND COMPUTEEFFICIENCY 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) descriptio n to the basic advection-diffusion equation for the concentration of m icro pollutant consists in modelling the micro pollutant particles' tr ajectories as a diffusion stochastic process. Indeed, the density of t his latter satisfies the same Pde as the advection-diffusion equation. Our emphasis here is on the computation of the so called tank efficie ncy and on the bottom boundary conditions. We claim that our interpret ation in terms of a diffusion process helps to enlighten the choice of the appropriate mathematical boundary conditions. What is more, we in troduce a scouring parameter and give its range as well as its physica l interpretation.