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Contour dynamics for the Euler equations: Curvature controlled initial node placement and accuracy. (English) Zbl 0649.76010
We have performed a systematic study of several contour dynamical algorithms for the Euler equations for short times. We have used the Kirchhoff elliptical vortex alone and subject to weak perturbations. We have found that if the initial placement of nodes is such that the internodal distance is proportional to \((curvature)^{-p}\) where \(p\approx 1/3\), then errors in short time calculations are minimized. This follows because the node density is invariant in time.

MSC:
76B47 Vortex flows for incompressible inviscid fluids
65Z05 Applications to the sciences
76M99 Basic methods in fluid mechanics
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