The collisionless expansion of ccounterstreaming plasmas has been studied by solving the self-consistent set of Vlasov and Poisson equations in one dimension. The motivation for the study is to elucidate some of the basic physical processes which may occur during the initial refilling of depleted flux tubes after a magnetic storm. The simulation geometry consisted of two high-density H+-O+-electron plasmas (conjugate ionospheres) separated by a low density H+-electron plasma (equatorial plasmasphere). The temporal evolution of the expandinng plasmas and the electrostatic potential in the region between the two sources hass the following characteristics. The initially minor H+ ions rapidly flow out of the source regions, creating counterstreaming density shock fronts which propagate at the Sagdeev Mach number for ion acoustic shocks (M~1.6). However, the shocks are preceded by suprathermal forerunner ions, which are the first to fill the ''equatorial'' region. When the counterstreaming ion acoustic shocks collide, the density in the equatorial region becomes nearly a constant, twice the value of the density in the individual shocks. The electrostatic potential distribution from the source plasmas to the midpoint of the expansion region displays an interesting feature. A potential hill forms near the midpoint after the arrival of the main density shock fronts. This localized potential hill plays an important role in the thermalization of the ion streams and may occur in the equatorial plasmasphere after magnetic storms. The numerical simulations indicate that the ion beams in the counterstreaming plasmas are remarkably stable with respect to the ion acoustic instability, which is in agreement with the linear instability theory. However, in the presence of a magnetic field, the linear instability theory predicts that the counterstreaming suprathermal forerunner ions can excite ion cyclotron waves, which in turn can thermalize and trap the suprathermal forerunners. Such a mechanism may be operating in the equatorial plasmasphere shortly after magnetic storms.