ABSTRACT GRB 030329 displays one clear and, possibly, multiple less intense fast-rising (Δt/t ∼ 0.3) jumps in its optical afterglow light curve. The decay rate of the optical light curve remains the same before and after the flux jumps. This may be the signature of energy injection into the shocked material at the front of the jet. In this study, we model the Gamma-ray Burst (GRB) ejecta as a series of shells. We follow the dynamical evolution of the ejecta as it interacts with itself (i.e. internal shocks) and with the circumburst medium (i.e. external forward and reverse shocks), and calculate the emission from each shock event assuming synchrotron emission. We confirm the viability of the proposed model in which the jumps in the optical afterglow light curve of GRB 030329 are produced via refreshed shocks. The refreshed shocks may be the signatures of collisions between earlier ejected material with an average Lorentz factor $\bar{\Gamma }\gtrsim 100$ and later ejected material with $\bar{\Gamma } ∼ 10$ once the early material has decelerated due to interaction with the circumburst medium. We show that even if the late material is ejected with a spread of Lorentz factors, internal shocks naturally produce a narrow distribution of Lorentz factors (ΔΓ/Γ ≲ 0.1), which is a necessary condition to produce the observed quick rise times of the jumps. These results imply a phase of internal shocks at some point in the dynamical evolution of the ejecta, which requires a low magnetization in the outflow.