A Lattice Boltzmann Method for the Advection-Diffusion Equation with Neumann Boundary Conditions (Communications in Computational Physics, 2018)
In this paper, we study a lattice Boltzmann method for the advection-diffusion equation with Neumann boundary conditions on general boundaries. Anovel mass conservative scheme is introduced for implementing such boundary conditions, and is analyzed both theoretically and numerically.Second order convergence is predicted by the theoretical analysis, and numericalinvestigations show that the convergence is at or close to the predicted rate. The numerical investigations include time-dependent problems and a steady-state diffusionproblem for computation of effective diffusion coefficients.