A multi-dimensional model is presented for simulating overland and riverine flows using the Saint-Venant equations (SVE) and their approximations, such as the kinematic wave (KWE) and diffusive wave (DWE). This thesis investigates conditions where the approximations to the SVE for overland and riverine flow are applicable. A sensitivity analysis is performed for the overland flow module. Additionally, the channel flow modules are run on hundreds of compound flood simulations. The Froude and Kinematic numbers for each simulation are analyzed using these findings, and new computational bounds are developed. Lastly, the physical characteristics of rivers are compared to the average values of the pressure gradient term in the DWE. Results suggest that longer rivers and higher slopes result in higher values of the pressure gradient term, indicating the DWE results in better approximations than the KWE in these conditions, and the KWE may not be applicable for high slopes.