- An asymptotic theory of spiral density waves and their instabilities in the Saturnian ring system of mutually gravitating and colliding particles has been developed (Griv et al. 2000, Pl&SS, 48, 679-698). The theory is successfully applied to interpreting the observations of the fine-scale structure of Saturn's rings. Our aim is to confirm the validity of the theory by computer many-body (N-body) calculations. As is known, N-body models of Saturn's rings suffer from graininess due to the finite number of particles in direct simulations; the graininess manifests itself as a numerical noise in the calculation. For the first time in planetary ring dynamics, we change the existing direct simulation code. This change involves multiprocessing: with the multiple processors in supercomputers it is possible to reduce the running time by processing more than one group of particles at a time. Use of the 112-processor SGI Origin 2000 supercomputer is enabled us to make long runs using realistic numbers of particles in the direct simulation code and thus simulate phenomena not previously studied numerically. The study will be held in order to predict the ``hyperfine" Saturn's ring system structure of the order 100 m or even less prior to its exploration by Cassini spacecraft that will start in 2004. Partial support for this work was provided by the Israel Science Foundation, the Israeli Ministry of Immigrant Absorption, and the Academia Sinica in Taiwan.