  In this paper, we perform a more general analysis on the discrete effects of
some boundary schemes of the popular one- to three-dimensional DnQq
multiple-relaxation-time lattice Boltzmann model for convection-diffusion
equation (CDE). Investigated boundary schemes include anti-bounce-back(ABB)
boundary scheme, bounce-back(BB) boundary scheme and non-equilibrium
extrapolation(NEE) boundary scheme. In the analysis, we adopt a transform
matrix $\textbf{M}$ constructed by natural moments in the evolution equation,
and the result of ABB boundary scheme is consistent with the existing work of
orthogonal matrix $\textbf{M}$. We also find that the discrete effect does not
rely on the choice of transform matrix, and obtain a relation to determine some
of the relaxation-time parameters which can be used to eliminate the numerical
slip completely under some assumptions. In this relation, the weight
coefficient is considered as an adjustable parameter which makes the parameter
adjustment more flexible. The relaxation factors associated with second moments
can be used to eliminate the numerical slip of ABB boundary scheme and BB
boundary scheme while the numerical slip can not be eliminated of NEE boundary
scheme. Furthermore, we extend the relations to complex-valued CDE, several
numerical examples are used to test the relations.
