  We present a fully parallel chemo-dynamical Tree/SPH code, GEAR, which allows
to perform high resolution simulations with detailed chemical diagnostics.
Starting from the public version of Gadget-2, we included the complex treatment
of the baryon physics: gas cooling, star formation law, chemical evolution and
supernovae feedback. We qualified the performances of GEAR with the case of
dSph galaxies. GEAR conserves the total energy budget of the systems to better
than 5% over 14Gyr and proved excellent convergence of the results with
numerical resolution. We showed that models of dSphs in a static Euclidean
space, where the expansion of the universe is neglected are valid. In addition,
we tackled some of the existing open questions in the field, like the stellar
mass fraction of dSphs and its link with the predicted dark matter halo mass
function, the effect of the supernova feedback, the spatial distribution of the
stellar populations, and the origin of the diversity in star formation
histories and chemical abundance patterns. Strong supernovae driven winds seem
incompatible with the observed metallicities and luminosities. Despite the fact
that newly formed stars are preferentially found in the galaxy central parts,
turbulent motions in the gas can quickly erase any metallicity gradient. The
variety in dSph properties result from a range of total masses as well as from
a dispersion in central densities. The latter is also seen in the haloes
emerging from a LCDM cosmogony.
