  We present a novel Dynamic Monte Carlo code (DynaMo code) which
self-consistently simulates the Compton scattering driven dynamic evolution of
a plasma. We use the DynaMo code to investigate the time-dependent expansion
and acceleration of dissipationless GRB fireballs by varying their initial
opacities and baryonic content. We study the opacity and energy density
evolution of an initially optically thick, radiation-dominated fireball across
its entire phase space - in particular during the $R_{\rm ph} < R_{\rm sat}$
regime. Our results reveal new phases of fireball evolution: a transition phase
with a radial extent of several orders of magnitude - the fireball transitions
from $\Gamma \propto R$ to $\Gamma \propto R^0$, a post-photopsheric
acceleration phase - where fireballs accelerate beyond the photosphere, and a
Thomson-dominated acceleration phase - characterized by slow acceleration of
optically thick, matter-dominated fireballs due to Thomson scattering. We
quantify the new phases by providing analytical expressions of Lorentz factor
evolution, which will be useful for deriving jet parameters.
