Extended analysis of a pseudo-spectral approach to the vortex patch problem

Abstract: A prestudy indicated superior accuracy and convergence properties of apseudo-spectral method compared to a spline-based method implemented byCòrdoba et al. in 2005 when solving the α-patches problem. In this thesis wefurther investigate the numerical properties of the pseudo-spectral method and makeit more robust by implementing the Nonequispaced Fast Fourier Transform. Wepresent a more detailed overview and analysis of the pseudo-spectral method and theα-patches problem in general and conclude that the pseudo-spectral method issuperior in regards to accuracy in periodic settings.