Lattice Boltzmann Method for 2D Tidal Flow: Application to the Nador Lagoon (Advances in Applied Mathematics and Mechanics, 2025)
The lattice Boltzmann method is a relatively modern method. It has beenwidely applied to industrial flows (for small scales) governed by the Navier Stokesequations, but little applied to large-scale flows, such as geophysical flows. In this paper, we then attempt to apply the lattice Boltzmann method to coastal flows governedby the Saint-Venant equations (also called Shallow water equations) via an applicationto the real case of the Nador lagoon (Moroccan Mediterranean coast).The establishment of the equations of the model and their discretization is given here.The introduction of turbulence by the large eddy simulations was also presented. Theverification of the developed code concerns two test cases in hydraulic engineering.The first verification test deals with complex flow in a $180^◦$ bent channel. For thiscase, the model has faithfully reproduced all the characteristics of this flow (pressure/depression zone and the recirculation zone after the bend). Similarly, the resultsof this test case have been successfully compared to measurements available in the literature. The second verification test analyzes the flow around a spur-dike. Finally, thedeveloped code has been adapted for its application to the real case of the Nador lagoon whose flow is generated by the superposition of the tidal waves $M_2$ and $S_2.$ Themodel reproduced with good accuracy the dynamics of the flow and more particularlythe two vortices observed on both sides of the lagoon inlet. The founding results aresuccessfully compared with the results of previous studies published for the lagoon.