  It is well known that chaotic dynamic systems (such as three-body system,
turbulent flow and so on) have the sensitive dependence on initial conditions
(SDIC). Unfortunately, numerical noises (such as truncation error and round-off
error) always exist in practice. Thus, due to the SDIC, long-term accurate
prediction of chaotic dynamic systems is practically impossible. In this paper,
a new strategy for chaotic dynamic systems, i.e. the Clean Numerical Simulation
(CNS), is briefly described, together with its applications to a few
Hamiltonian chaotic systems. With negligible numerical noises, the CNS can
provide convergent (reliable) chaotic trajectories in a long enough interval of
time. This is very important for Hamiltonian systems such as three-body
problem, and thus should have many applications in various fields. We find that
the traditional numerical methods in double precision cannot give not only
reliable trajectories but also reliable Fourier power spectra and
autocorrelation functions. In addition, it is found that even statistic
properties of chaotic systems can not be correctly obtained by means of
traditional numerical algorithms in double precision, as long as these
statistics are time-dependent. Thus, our CNS results strongly suggest that one
had better to be very careful on DNS results of statistically unsteady
turbulent flows, although DNS results often agree well with experimental data
when turbulent flows are in a statistical stationary state.
