Contour dynamics for the Euler equations: Curvature controlled initial node placement and accuracy
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.
curvature controlled initial node placement
scientific article; zbMATH DE number 4060863