Cosmological simulations still lack numerical resolution or physical processes to simulate dwarf galaxies in sufficient details. Accurate numerical simulations of individual dwarf galaxies are thus still in demand. We aim at (i) studying in detail the coupling between stars and gas in a galaxy, exploiting the so-called stellar hydrodynamical approach, and (ii) studying the chemo-dynamical evolution of individual galaxies starting from self-consistently calculated initial gas distributions. We present a novel chemo-dynamical code in which the dynamics of gas is computed using the usual hydrodynamics equations, while the dynamics of stars is described by the stellar hydrodynamics approach, which solves for the first three moments of the collisionless Boltzmann equation. The feedback from stellar winds and dying stars is followed in detail. In particular, a novel and detailed approach has been developed to trace the aging of various stellar populations, which enables an accurate calculation of the stellar feedback depending on the stellar age. We build initial equilibrium models of dwarf galaxies that take gas self-gravity into account and present different levels of rotational support. Models with high rotational support develop prominent bipolar outflows; a newly-born stellar population in these models is preferentially concentrated to the galactic midplane. Models with little rotational support blow away a large fraction of the gas and the resulting stellar distribution is extended and diffuse. The stellar dynamics turns out to be a crucial aspect of galaxy evolution. If we artificially suppress stellar dynamics, supernova explosions occur in a medium heated and diluted by the previous activity of stellar winds, thus artificially enhancing the stellar feedback (abridged).
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