  Accelerated coarse-graining (CG) algorithms for simulating heterogeneous
chemical reactions on surface systems have recently gained much attention. In
the present paper, we consider such an issue by investigating the oscillation
behavior of a two-dimension (2D) lattice-gas Brusselator model. We have adopted
a coarse-grained Kinetic Monte Carlo (CG-KMC) procedure, where $m \times m$
microscopic lattice sites are grouped together to form a CG cell, upon which CG
processes take place with well-defined CG rates. We find that, however, such a
CG approach almost fails if the CG rates are obtained by a simple local mean
field ($s$-LMF) approximation, due to the ignorance of correlation among
adjcent cells resulted from the trimolecular reaction in this nonlinear system.
By properly incorporating such boundary effects, we thus introduce the
so-called $b$-LMF CG approach. Extensive numerical simulations demonstrate that
the $b$-LMF method can reproduce the oscillation behavior of the system quite
well, given that the diffusion constant is not too small. In addition, we find
that the deviation from the KMC results reaches a nearly zero minimum level at
an intermediate cell size, which lies in between the effective diffusion length
and the minimal size required to sustain a well-defined temporal oscillation.
