A mesoscopic coupling scheme for solute transport in surface water using the lattice boltzmann method

Abstract

A one-dimensional (1D) and two-dimensional (2D) coupling procedure for solute transport is presented using the lattice Boltzmann method (LBM). It makes use of the advantage of the LBM boundary treatment and avoids the boundary control-volume problems of the traditional computational fluid dynamics (CFD) methods, such as the high order finite difference method (FDM) and the finite volume method (FVM). The proposed coupling scheme only uses the solute particle distributions and kinetic velocities at current time to calculate the missing particle distributions at the boundary lattices. Concentration variables can then be derived from the mesoscopic particle quantities according to the particle group definition equation in the LBM. The calculation is locally dependent and simultaneous, so the coupling scheme can be performed right after the calculation of each single dimensional model. No asynchronous variables are involved and no further lattice is related to the coupling. This can keep the advantage of parallel computation of the LBM and bring the simplicity of the boundary treatment of the LBM to deal with solute transport problems. The model is tested by three benchmarks: point source solute transported in steady flow, diffusion through a square cavity and a sharp curved flow. The results show that the 1D-2D coupling model has a good agreement with the analytical solution in the point source transportation, and is also able to qualitatively approximate the results achieved by a pre-verified full 2D LBM model. It is not only an accurate and efficient coupling scheme, but also a new cross-dimensional coupling method in water quality simulation.