Some ultra-high energy ( UHE ) cosmic ray ( CR ) events may be correlated with the Local Supercluster plane .
We consider acceleration of such particles at the large-scale accretion flows of matter towards such plane and/or accretion flows onto galaxy clusters .

The formed shocks and the general compression flow are expected to allow for CR diffusive acceleration of UHE particles .
For a simplified flow geometry we consider a stationary acceleration of such CRs and we discuss influence of model parameters on a particle spectral index .
We show that the general convergent flow pattern leads naturally to very flat proton spectra with the phase-space spectral indices \sigma \approx 3.0 , as compared to the ‘ canonical ’ shock value of 4.0 .