A coupled lattice Boltzmann model for advection and anisotropic dispersion problem in shallow water

A coupled lattice Boltzmann model (CLBM) for 2D advection and anisotropic dispersion equation (AADE) and shallow water equations is formulated and implemented. Multi-relaxation-time (MRT) method is used for the flow field and the L  -basis two-relaxation-time (TRT) method is used for the pollutant field. The relaxation time for the antisymmetric part of the pollutant deviates from a constant for flows with variable free surface water depth. Numerical tests show that this scheme strictly obeys conservation of mass and momentum. And the model has a better accuracy when τDτD is closer to 12 and τeτe is closer to ∑τD∗9. Excellent agreement is obtained between numerical predictions and analytical solutions in pure dispersion problem and advection–dispersion problem. Comparison with finite different method indicates that the variation of the free surface water depth does not affect the mass and momentum conservation of the model and that the model has the ability to simulate complex bed topography problem. Comparison with finite volume method in the 2D steady flow around a rectangular column with non-slip boundary shows that the LB scheme has the capacity to solve the complex advection–dispersion problems in shallow water.