Evolutions of X-ray clusters of galaxies are studied by N-body ( shell model ) + mesh code ( TVD ) simulations on the assumption of spherical symmetry .
We consider a density perturbation of 10 ^ { 15 } M _ { \odot } composed of dark matter and gas in cold dark matter dominated universe with the cosmological density parameter , \Omega _ { 0 } = 1 or 0.2 .
A shock front appears during its initial collapse , moving outward as ambient gas accretes towards cluster center .
The shock front separates the inner X-ray emitting , hot region , where gas is almost in hydrostatic equilibrium but with small radial infall ( \sim 100 km s ^ { -1 } ) being left , from the outer cool region , where gas falls almost freely and emits no X-rays .
Gas inside the shock is strongly compressed and heated by shock so that X-ray luminosity rapidly rises in the early stage ( until temperature reaches about virial ) .
In the late stage , however , the X-ray luminosity rises only gradually due partly to the expansion of the inner high temperature region and partly to the increase of X-ray emissivity of gas as the results of continuous adiabatic compression inside the shock .
We also find for clusters in lower density universe that the density distribution is generally less concentrated and , hence , X-ray luminosity more slowly rises than in higher density universe .

The shock front structure , which was not clearly resolved in the previous SPH simulations , is clearly captured by the present simulations .
Our results confirm that shock heating plays an important role in the heating process of intracluster medium .
In addition , we find a sound wave propagating outward , thereby producing spatial modulations with amplitudes of \sim 10 % in the radial temperature and density profiles and time variations in the strength of the shock .
Such modulations , if observed , could be used as a probe to investigate the structure of clusters .