Saturn's magnetosphere is unique in the solar system. The rotation-driven convection consists of alternating channels of cool plasma from an interior source moving outward and hot plasma from outside moving inward, making Saturn’s inner magnetosphere a dynamical region. This thesis describes work on developing numerical models to simulate the plasma convection pattern in Saturn's inner magnetosphere. Chapter 2 introduces the numerical Rice Convection Model (RCM), a multi-fluid model that was originally developed for Earth’s magnetosphere. We adapt it for Saturn’s conditions in this thesis. In Chapter 3, we show results of initial RCM simulation runs, in which only cool plasma from the interior source is considered. We also include the Coriolis force and the pickup effect. Because the cool plasma is much denser than the hot plasma and always dominant in determining the convection pattern, it is important and necessary to investigate it first. Chapter 4 compares several cool plasma source models and determines the one that produces the best simulation results when compared to Cassini spacecraft observations. In Chapter 5, we add the finite temperature and associated plasma pressure of the cool plasma. The effect of ionospheric Pedersen conductance is also investigated. Finally in Chapter 6, we add hot plasma at the outer boundary, and simulate the V-shape signatures of the injection-dispersion events, which are considered the most definitive evidence of rotation-driven convection in Saturn's inner magnetosphere. Our simulations conform to the observed fact that wider, slower outflow channels of cooler, denser plasma alternate with narrower, faster inflow channels of hotter, more tenuous plasma. Comparisons between simulated and observed results show great consistency.