  Epitaxial growth via chemical vapor deposition is considered to be the most
promising way towards synthesizing large area graphene with high quality.
However, it remains a big theoretical challenge to reveal growth kinetics with
atomically energetic and large-scale spatial information included. Here, we
propose a minimal kinetic Monte Carlo model to address such an issue on an
active catalyst surface with graphene/substrate lattice mismatch, which
facilitates us to perform large scale simulations of the growth kinetics over
two dimensional surface with growth fronts of complex shapes. A
geometry-determined large-scale growth mechanism is revealed, where the
rate-dominating event is found to be $C_{1}$-attachment for concave growth
front segments and $C_{5}$-attachment for others. This growth mechanism leads
to an interesting time-resolved growth behavior which is well consistent with
that observed in a recent scanning tunneling microscopy experiment.
