We study the properties of cosmological shock waves identified in high-resolution, N-body/hydrodynamic simulations of a $Lambda$CDM universe and their role on thermalization of gas and acceleration of nonthermal, cosmic ray (CR) particles. External shocks form around sheets, filaments and knots of mass distribution when the gas in void regions accretes onto them. Within those nonlinear structures, internal shocks are produced by infall of previously shocked gas to filaments and knots, and during subclump mergers, as well as by chaotic flow motions. Due to the low temperature of the accreting gas, the Mach number of external shocks is high, extending up to $Msim 100$ or higher. In contrast, internal shocks have mostly low Mach numbers. For all shocks of $Mge1.5$ the mean distance between shock surfaces over the entire computed volume is $sim4 h^{-1}$ Mpc at present, or $sim 1 h^{-1}$ Mpc for internal shocks within nonlinear structures. Identified external shocks are more extensive, with their surface area $sim2$ times larger than that of identified internal shocks at present. However, especially because of higher preshock densities, but also due to higher shock speeds, internal shocks dissipate more energy. Hence, the internal shocks are mainly responsible for gas thermalization as well as CR acceleration. In fact, internal shocks with $2 la M la 4$ contribute $sim 1/2$ of the total dissipation. Using a nonlinear diffusive shock acceleration model for CR protons, we estimate the ratio of CR energy to gas thermal energy dissipated at cosmological shock waves to be $sim1/2$ through the history of the universe. Our result supports scenarios in which the intracluster medium contains energetically significant populations of CRs.
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