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

Implementation of nonlinear boundary conditions like n(th)-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 l(2)-norm analyses showed first or second-order rates of convergence, depending on constraint's degree of nonlinearity. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

A novel kinetic level method is proposed in this study to implement nonlinear boundary conditions such as n(th)-order surface reactions or surface radiation heat transfer. The method combines Taylor expansion of the conditions with a counter-slip approach to find unknown distribution functions at boundary nodes. Experimental results show promising performance in terms of accuracy and convergence speed when dealing with surface reactions and radiation heat transfer.