I propose a numerical model which describes the dynamical features of
vibrated beds. It succeeds in reproducing convective motion in vibrate
d beds which was observed by Faraday for the first time in 1831. In ad
dition to this, this modeling can explain threshold value of instabili
ty and surface fluidization. Moreover, I numerically show vibrated bed
without side wall can exhibit strong non-linear feature like turbulen
ce or anomalous diffusion.