A Comparison of the contour surgery and pseudo-spectral methods

Two very different numerical methods which have been used to simulate high Reynolds number two-dimensional flows are compared for the first time. One method, the pseudo-spectral method, is fundamentally based on the Eulerian description of fluid flow and the other, the contour surgery method, is inherently Lagrangian. The former makes use of a continuous distribution of vorticity, while the latter, a theoretically inviscid method, makes use of a discrete distribution. A comparison is nevertheless attempted in a model problem wherein the initial vorticity distribution is continuous. We examine the stripping of an initially circular vortex by applied adverse shear in doubly periodic geometry. The constraining geometry causes the flow to become very complex, placing great demands on both computational methods. The surprise is that as few as eight discrete levels of vorticity in contour surgery five results which are quantitatively close to those obtained by the pseudo-spectral method at high resolution. Advantages and shortcomings of both methods are noted.