Numerical Study Of Water Circulation In Shallow Basin Using Lattice Boltzmann Method

Abstract

Abstract In the present work, a code based on the Lattice Boltzmann method (LBM) has been developed to study the hydrodynamic field in a shallow basin with complicated geometry. It is a non-regular border basin with dikes built inside. The LBM method was therefore used to solve the Navier Stokes equations with boundary conditions which express that the components of the horizontal two-dimensional velocity field are zero at closed boundaries (sealing and non-slip conditions), while the flow is imposed at the entrance of the basin, and a zero speed gradient is imposed at the free exit of the basin (condition of continuity of the flow). The validation of the developed code was verified by comparing the results obtained with those of Charafi et al. [5], where the finite difference method with a MacCormack scheme was used. A good agreement of the results was noted. A series of simulations was made for different values of the Reynolds number, and showed good performance of the code. The main advantage of the LBM method seen in this work lies in the simplicity of its implementation. However, the model suffers from some limitations such as its validity for low Reynolds numbers (Re = 400)