A Lattice Boltzmann Method for the Advection-Diffusion Equation with Neumann Boundary Conditions

Journal article, 2014

In this paper, we study a lattice Boltzmann method for the advection-diffusion equation with Neumann boundary conditions on general boundaries. A novel mass conservative scheme is introduced for implementing such boundary con- ditions, and is analyzed both theoretically and numerically. Second order convergence is predicted by the theoretical analysis, and numerical investigations show that the convergence is at or close to the predicted rate. The nu- merical investigations include time-dependent problems and a steady-state diffusion problem for computation of effective diffusion coefficients.