Why is the Zel'dovich Approximation so Accurate?
  Why does the Zel'dovich approximation (ZA) work well to describe gravitational collapse in the universe? This problem is examined by focusing on its dependence on the dimensionality of the collapse. The ZA is known to be exact for a one-dimensional collapse. We show that the ZA becomes progressively more accurate in the order of three-, two-, and one-dimensional collapses. Furthermore, using models for spheroidal collapse, we show that the ZA remains accurate in all collapses, which become progressively lower dimensional with the passage of time. That is, the ZA is accurate because the essence of the gravitational collapse is incorporated in the ZA. 
A. Yoshisato, M. Morikawa, N. Gouda, H. Mouri