  Cosmological hydrodynamic simulations of large scale structure in the
universe have shown that accretion shocks and merger shocks form due to flow
motions associated with the gravitational collapse of nonlinear structures.
Estimated speed and curvature radius of these shocks could be as large as a few
1000 km/s and several Mpc, respectively. According to the diffusive shock
acceleration theory, populations of cosmic-ray particles can be injected and
accelerated to very high energy by astrophysical shocks in tenuous plasmas. In
order to explore the cosmic ray acceleration at the cosmic shocks, we have
performed nonlinear numerical simulations of cosmic ray (CR) modified shocks
with the newly developed CRASH (Cosmic Ray Amr SHock) numerical code. We
adopted the Bohm diffusion model for CRs, based on the hypothesis that strong
Alfv\'en waves are self-generated by streaming CRs. The shock formation
simulation includes a plasma-physics-based ``injection'' model that transfers a
small proportion of the thermal proton flux through the shock into low energy
CRs for acceleration there. We found that, for strong accretion shocks, CRs can
absorb most of shock kinetic energy and the accretion shock speed is reduced up
to 20 %, compared to pure gas dynamic shocks. For merger shocks with small Mach
numbers, however, the energy transfer to CRs is only about 10-20 % with an
associated CR particle fraction of $10^{-3}$. Nonlinear feedback due to the CR
pressure is insignificant in the latter shocks. Although detailed results
depend on models for the particle diffusion and injection, these calculations
show that cosmic shocks in large scale structure could provide acceleration
sites of extragalactic cosmic rays of the highest energy.
