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Simulations are used here to show that the hierarchical tree method can faithfully reproduce the statistical behavior of systems undergoing clustering through gravitational instability. The influence of the approximation in the potential, the two-body softening length, the time-step, and the particle number on the resulting evolution is investigated in order to infer the properties of the method for future applications. Various schemes for handling boundary conditions are briefly discussed. It is shown that the efficiency of the technique is insensitive to the degree of clustering present in the simulations. Hence, the hierarchical tree method may be superior to more traditional N-body algorithms for evolving strongly nonlinear systems requiring a large particle number and dynamical range.
Bouchet et al. (Thu,) studied this question.