Multi-block lattice Boltzmann simulations of solute transport in shallow water flows

• A 2-D multi-block lattice Boltzmann scheme for solute transport is developed.
• A new approach to deal with the external forces is presented.
• A coupled multi-block LBM for shallow water flows and solute transport is built.
• The application to Baiyangdian Lake shows good potential of the model in practice.
• The revised slip boundary condition is easier to implement for the circular domain.

We report a two-dimensional multi-block lattice Boltzmann model for solute transport in shallow water flows, which is developed based on the advection–diffusion equation for mass transport and the shallow water equations for the flows. A weighting factor is included in the centered scheme for improved accuracy. The model is firstly verified by simulating three benchmark tests: wind-driven circulation in a dish-shaped lake, jet-forced flow in a circular basin, and flow formed by two parallel streams containing different uniform concentrations at the same constant velocity; and then it is applied to a practical wind-induced flow, Baiyangdian Lake, which is characterized by irregular geometries and complex bathymetries. The numerical results have shown that the model is able to produce accurate and detailed results for both water flows and solute transport, which is attractive, especially for flows in narrow zones of practical terrains and certain areas with largely varying pollutant concentrations.