Local reactive boundary scheme for irregular geometries in lattice Boltzmann method

In this paper, a boundary scheme is proposed for the lattice Boltzmann method for convection-diffusion problems in irregular geometries with linear heterogeneous surface reaction. Compared with previous schemes, the physical picture of the proposed one is more clear, which reflects the consumption and production of the reaction at the boundary. Furthermore, as the unknown distribution functions at the boundary nodes are determined locally based on the kinetic flux of the incident ones, the present scheme can be easily applied to problems with complex geometric structures. The accuracy of the scheme is first tested by simulating the transient longitudinal mixing phenomenon and the convection-diffusion problems in inclined channels. The numerical results are in excellent agreement with the analytical solutions, and it is shown that the boundary scheme is of second-order accuracy in space for a straight wall in line with a link of the lattice. However, the order of accuracy will decrease for a general irregular wall. Finally, the dissolution process of a single calcite grain is simulated in both two-dimension (2D) and three-dimension (3D). Although a slight difference was observed between the results of 2D and 3D, all the results agree well with experimental measurements reported in previous study.