Non-linear boundary conditions for the convection-diffusion equation in lattice Boltzmann framework

Abstract

Implementation of nonlinear boundary conditions like nth-order surface reactions or surface radiation heat transfer has not been investigated in lattice Boltzmann (LB) framework. This study presents a novel kinetic level method for their implementation. The method couples Taylor expansion of the conditions with counter-slip approach to find unknown distribution functions at boundary nodes. The proposed scheme guarantees the locality and orientation independency of formulations. To evaluate the proposed scheme performance, several 1D and 2D test cases were simulated by D2Q9 LBM and the outcomes were compared with analytical and numerical solutions. The geometry evolution by nth-order surface reaction was investigated for dissolutions in a simple fracture and a spherical carbonate particle in a channel. The results demonstrated the method performs promisingly in terms of accuracy. The convergence rate of scheme based on the results from l2-norm analyses showed first or second-order rates of convergence, depending on constraint’s degree of nonlinearity.