The supermassive black hole, Sagittarius A* (Sgr A*), at the centre of the Milky Way undergoes regular flaring activity which is thought to arise from the innermost region of the accretion flow. We performed the monitoring observations of the Galactic Centre to study the flux-density variations at 3mm using the Australia Telescope Compact Array (ATCA) between 2010 and 2014. We obtain the light curves of Sgr A* by subtracting the contributions from the extended emission around it, and the elevation and time dependent gains of the telescope. We perform structure function analysis and the Bayesian blocks representation to detect flare events. The observations detect six instances of significant variability in the flux density of Sgr A* in three observations, with variations between 0.5 to 1.0 Jy, which last for 1.5 $-$ 3 hours. We use the adiabatically expanding plasmon model to explain the short time-scale variations in the flux density. We derive the physical quantities of the modelled flare emission, such as the source expansion speed $v_{mathrm{exp}}$, source sizes, spectral indices, and the turnover frequency. These parameters imply that the expanding source components are either confined to the immediate vicinity of Sgr A* by contributing to the corona or the disc, or have a bulk motion greater than $v_{mathrm{exp}}$. No exceptional flux density variation on short flare time-scales was observed during the approach and the flyby of the dusty S-cluster object (DSO/G2). This is consistent with its compactness and the absence of a large bow shock.
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