Analysis of Coupled Lattice Boltzmann Model with Well-Balanced Scheme for Shallow Water Flow

Abstract

The coupled lattice Boltzmann method (CLBM) is applied in investigating contamination transport in shallow water flows. Shallow water equations and advection-diffusion equation are both solved using lattice Boltzmann method (LBM) on a D2Q9 square lattice and Bhatnagar-Gross-Krook (BGK) term. For extending application of CLBM in shallow water flows, the well-balanced scheme is introduced to replace the source term. Three cases including dam break, 2D pure diffusion and complex tidal flow are calculated and analyzed. Dam break and 2D pure diffusion are prepared to validate the flow module and water quality module, respectively. Both the cases show satisfactory consistency between predicting results and analytical solutions. Since clear reproduction of the shock wave propagation and precise prediction of contamination transport are derived, LBM is proved to be the numerical method naturally conservative with acceptable computing error. Furthermore, complex tidal flow with irregular geometry and sinus-varied bathymetry is simulated by adopting the well-balanced treating on the source term. The velocity fields, water levels, and water quality are compared between the ebb tide and flood tide, the results of which are in excellent accordance with the physical laws during the process. Hence, it may demonstrate that improved by well-balanced scheme CLBM can be widely applicable in shallow water flow.