Lattice Boltzmann simulation of pollutant transport in shallow water flows: Application to Nador lagoon

Abstract

This paper present a novel numerical method based on lattice Boltzmann and designed for simulating pollutant transport in Nador lagoon (Moroccan eastern coast of Mediterranean Sea). The model solves the shallow water equations coupled to the depth-averaged advection-diffusion equation. Solution of the Shallow water equations was performed by the multiple relaxation time lattice Boltzmann method, while the depth-averaged advection-diffusion equation was solved by the single relaxation time lattice Boltzmann method. To keep its role of mixing processes, the diffusion coefficients were determined by a linear relationship from the turbulent viscosity via the Schmit number. This relationship allowed the link of the relaxation time of hydrodynamics and the relaxation time of diffusion processes.

The results of the numerical hydrodynamic model were validated by comparison with laboratory measurements treating flow in two-branches channels. The analysis of this comparison showed that our numerical model reproduces this flow with high precision. Furthermore, the numerical solution of advection-diffusion equation was validated by comparison with both stationary and unsteady analytical solutions. The error analysis also showed that the proposed numerical model simulates the propagation of a contaminant with good accuracy.

After the validation phase, the numerical model was applied to simulate the propagation of pollutant for the real case of the Nador lagoon. For this case, the sources of pollution were identified at the positions of the different waterways bordering the southern shore of the lagoon. Two hydrodynamic scenarios were simulated: flow without wind and flow with wind. In the absence of measurement data on the area, the qualitative analysis of the simulation results showed consistency both with the literature on the study area and with the dynamics of the Eulerian circulation of the lagoon.