  The properties of cosmic shock waves are studied through numerical
simulations in two cosmological scenarios (SCDM and LCDM). The scaling
relations for the average radius and velocity associated with the accretion
shocks are somewhat different, yet qualitatively similar to the self similar
solutions for a flat Omega_M=1 universe. The energy supplied by infalling gas
at accretion shock waves is large enough to sustain production of abundant
cosmic ray populations if a viable acceleration mechanism can take place there.
Finally, in addition to shocks created by the encounter of the merging ICMs of
two clusters of galaxies, accretion shocks associated with the merging clusters
generate strong ``relic'' shocks which propagate through the ICM producing
additional heating of the ICM, and associated CR acceleration.
