Designing wings and rotor blades to mitigate the adverse effects of dynamic stall is of current interest. For example, unmanned air vehicles with vertical take-off and landing capability are particularly susceptible to dynamic stall as they operate entirely in the highly unsteady planetary boundary layer. The intense unsteady loads generated as the vehicle undergoes dynamic stall can lead to catastrophic failure as well as fatigue failure. A passive mechanism to mitigate dynamic stall is a desirable alternative to active control as it is simpler, robust, and economical. Innovative wing and rotor blade designs can be developed using numerical simulations and optimization techniques. The objective of this thesis is to compare and evaluate simulations of varying degrees of fidelity that can be utilized as part of designing dynamic-stall-resistant aerodynamic shapes. The unsteady Reynolds-Averaged Navier-Stokes (URANS) model is selected as the low-fidelity simulation model, whereas the detached eddy simulation is selected as high-fidelity simulation model. The unsteady flow characteristics of the NACA 0012 airfoil undergoing dynamic stall are investigated with computational fluid dynamics using the URANS equations with Menter's k-$\omega$ SST turbulence model and the detached eddy simulation (DES) at free-stream Reynolds number = 135,000, free-stream Mach number = 0.04, reduced frequency = 0.05 in a sinusoidal motion. The results are validated with published results from experiments and large eddy simulations (LES). The effectiveness of each model to capture the dynamic stall is discussed. Special emphasis is given to the various unsteady events that occur during the unsteady sinusoidal motion of an airfoil, such as laminar separation region, trailing edge flow reversal and the formation and convection of dynamic stall vortex.