Lattice Boltzmann method for the age concentration equation in shallow water

Water age is a critical parameter in reflecting the extent of water exchange. It represents the time that water parcels or contaminants are transported from source to current positions. In this study, an equilibrium distribution function for water age concentration is proposed within the Eulerian framework based on the existing theory of water age, and it can recover the age concentration equation. In addition, the lattice Boltzmann method for water age in the Lagrangian procedures is developed. This method also enables the Lagrangian age to be fundamentally simulated under computationally expensive conditions. In numerical tests, cubic and circular reservoirs with narrow inflow-outflow boundaries are used to verify the applicability of the model. Finally, the proposed approaches are applied to the Baiyangdian Lake, the biggest freshwater lake in northern China. The result is compared with that acquired by the Environmental Fluid Dynamic Code (EFDC) as well.