This project investigates the unsteady aerodynamic response of a rigidly pitching airfoil and a morphing airfoil undergoing periodic gusts using numerical simulations. The numerical simulations will be performed from both higher-order methods and industry-standard software to generate validation of the formulation of gusts. Understanding the effects of gusts on the lift and drag allows for control of the airfoil angle of attack to affect the lift and drag. The gusts are created through vortex shedding over a semi-cylinder, following established research methodologies to mimic animal aerodynamics. Different Strouhal numbers are simulated, informing the pitch frequency of the airfoil, with the purpose of mimicking the biomechanical thrust generated by aquatic and aerial animals. Along with the biomechanics-inspired motion, the inlet conditions are varied to provide a wide range of data that resembles normal conditions that the airfoil will experience in its use case. The simulations will provide insight on aerodynamic parameters to allow improvements in flight and vertical-axis turbine dynamics. These results will lead to further improvement to small Unmanned Aerial Vehicles (UAVs), as well as improved efficiency for wind-energy technology. Along with the investigation of the fluid dynamics, the results will inform usefulness of higher-order methods for simulations focused on gusts and vortex-shedding.