In this talk, I will discuss simulations of the  benchmark problem arising from shock clustering. The computation of coarsely self-similar flow turbulence can be modeled by Smoluchowski's dynamics with additive kernel K(x,y)=x+y. Long time numerical integration ap proach fails for getting the self-similar solutions due to the accumulated errors.
In contrast, dynamic renormalization and fixed point algorithms are applied to the results of shortly evolved dynamics, and successfully overcome these difficulties. These methods not only capture the asymptotic behavior of the exact self-similar solutions, but also approximate the first moments with errors in satisfaction.

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