Lattice Boltzmann Method for the Advection and Diffusion Equation in Shallow Water
Solute transport exists in most natural flows, which can be described by the advective-diffusive equation. In numerical modeling of such phenomenon, it is important to deal with irregular boundary and angular boundary points for hydrodynamic and water quality modeling. However, there is no clear control method for corner points in water quality modeling in existing literature. In this study, two-dimensional symmetrical flow in a cubic cavity with contaminant transport is investigated based on the presented control mechanisms: the lattice Boltzmann method for the advection and diffusion equation. For corner points of square cavity, a corner points controlling method proposed in this study shows great validity and reliability in the application of models.