Numerical simulations of galaxy clusters including two species-baryonic gas
and dark matter particles-are presented. A cold dark matter spectrum, Gaus
sian statistics, and hat universe are assumed. The dark-matter component is
evolved numerically by means of a standard particle mesh method. The evolu
tion of the baryonic component has been studied numerically by using a mult
idimensional (three-dimensional) hydrodynamical code based on modern high-r
esolution shock-capturing techniques. These techniques are specially design
ed for treating accurately complex flows in which shocks appear and interac
t. With this picture, the role of shock waves in the formation and evolutio
n of rich galaxy clusters is analyzed. Our results display two well-differe
ntiated morphologies of the shocked baryonic matter: filamentary at early e
pochs and quasi-spherical at low redshifts.