The study of coastal flows based on lattice Boltzmann method: application Oualidia lagoon

The lattice Boltzmann method (LBM) is a recent method widely used in the field of computational fluid dynamics. It was first presented for solving the Navier–Stokes equations. Since then, most of the advances of this method have been published with applications to flows in small-scale domains, but rarely applied to large-scale geophysical flows (flows governed by the shallow equations). The purpose of this paper is then to show that the LBM can be successfully applied for the simulation of large-scale flows such as the propagation of the tidal wave in the Oualidia lagoon (Moroccan Atlantic coast). Before presenting the results of our simulations, we applied the LBM to the classic hydraulic case of a mixed flow in a convergent domain (slightly variable Froude number). This case test has made it possible to measure the performance of the approach. It showed that this method provides solutions with good precision while reproducing the characteristics of a flow as complex as that of a convergent channel flow (change of regime: from subcritical to supercritical). The LBM was then applied to the real case to simulate both the propagation of the \({M}_{2}\) $M_2$ -tidal wave and the estimation of the associated residual velocity in the Oualidia lagoon. As the first results of this numerical modeling, the code developed has shown the capability and the efficiency of reproducing correctly the expected characteristics of tidal circulation in the concerned lagoon. Consequently, the LBM (and especially its GPU parallel version) can now be considered a serious alternative to the classical discretization methods such as the finite differences, finite elements and finite volumes methods.