We have examined the properties of shock waves in simulations of large scale structure formation .
Two cosmological scenarios have been considered : a standard cold dark matter model with \Omega _ { M } = 1 ( SCDM ) and a cold dark matter model with cosmological constant and \Omega _ { M } + \Omega _ { \Lambda } = 1 ( \Lambda CDM ) having \Omega _ { \Lambda } = 0.55 .
Large-scale shocks result from accretion onto sheets , filaments and knots of mass distribution on a scale of order of \sim 5 h ^ { -1 } Mpc in both scenarios .
Energetic motions , partly residual of past accretion processes and partly caused by current asymmetric inflow along filaments , end up generating additional shocks .
These extend on a scale of order of \sim 1 h ^ { -1 } Mpc and envelop and penetrate deep inside the clusters .
Also collisions between substructures inside clusters form merger shocks .
Consequently , the topology of the shocks is very complex and highly connected .
During cosmic evolution the comoving shock surface density decreases , reflecting the ongoing structure merger process in both scenarios .

Accretion shocks have very high Mach numbers , typically between 10 and a few \times 10 ^ { 3 } , when photo-heating of the pre-shock gas is not included .
The characteristic shock velocity is of order v _ { sh } ( z ) = H ( z ) \lambda _ { NL } ( z ) , where \lambda _ { NL } ( z ) is the wavelength scale of the nonlinear perturbation at the given epoch .
However , the Mach number for merger and flow shocks ( which occur within clusters ) is usually smaller , in the range \sim 3 - 10 , corresponding to the fact that the intracluster gas is hot ( i.e. , already shock heated ) .
Statistical fits of shock velocities around clusters as a function of cluster temperature give power-law functions in accord with those predicted by one-dimensional solutions .
On the other hand , a very different result is obtained for the shock radius , reflecting extremely complex shock structures surrounding clusters of galaxies in three-dimensional simulations .
The amount of in-flowing kinetic energy across the shocks around clusters , which represents the power available for cosmic-ray acceleration , is comparable to the cluster X-ray luminosity emitted from a central region of radius 0.5 h ^ { -1 } Mpc .
Considering their large size and long lifetimes , those shocks are potentially interesting sites for cosmic-ray acceleration , if modest magnetic fields exist within them .