We examine the low angular momentum flow model for Sgr A* using two-dimensional hydrodynamical calculations based on the parameters of the specific angular momentum and total energy estimated in the recent analysis of stellar wind of nearby stars around Sgr A*. The accretion flow with the plausible parameters is non-stationary and an irregularly oscillating shock is formed in the inner region of a few tens to a 160 Schwarzschild radii. Due to the oscillating shock, the luminosity and the mass-outflow rate are modulated by several per cent to a factor of 5 and a factor of 2–7, respectively, on time-scales of 1 h to 10 d. The flows are highly advected and the radiative efficiency of the accreting matter into radiation is very low, ∼10−5 to 10−3, and the input accretion rate yr−1 results in the observed luminosities ∼1036 erg s−1 of Sgr A* if a two-temperature model and the synchrotron emission are taken into account. The mass-outflow rate of the gas originating in the post-shock region increases with the increasing input specific angular momentum and ranges from a few to 99 per cent of the input accreting matter, depending on the input angular momentum. The oscillating shock is necessarily triggered if the specific angular momentum and the specific energy belong to or are located just nearby the range of parameters responsible for a stationary shock in rotating inviscid and adiabatic accretion flow. The time variability may be relevant to the flare activity of Sgr A*.