Boundary scheme for linear heterogeneous surface reactions in the lattice Boltzmann method.

Abstract

A boundary scheme is proposed to treat the linear heterogeneous surface reaction (i.e., general Robin boundary condition) for the lattice Boltzmann method (LBM) in this study. The basic idea of the present scheme is to compute the scalar variable gradient in the boundary condition with the moment of the nonequilibrium distribution functions. The unknown distribution functions on the boundary can then be obtained on the basis of the given boundary condition. For a straight wall, where the lattice nodes are located on the boundaries, both the scalar variable and its gradient can be expressed in terms of the distribution functions at the boundary node, and the scheme is purely local. The scheme is also extended to problems with a curved wall, in which a linear extrapolation is employed to realize the exact boundary position. A common feature of the two schemes lies in the easy treatment of the heterogenous reactions in comparison with existing methods. A number of simulations are performed to test the accuracy of the schemes. The results show that for flat walls the scheme can achieve second-order accuracy, while for curved walls the order of the accuracy is between 1.0 and 1.5.