An analytical and numerical study of axisymmetric flow around spheroids

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Abstract
Axisymmetric viscous flow around ellipsoids of circular section is studied in detail by the method of matched asymptotic expansion and a deterministic hybrid vortex method. The main feature of the hybrid vortex method consists in solving the viscous vorticity equation by interlacing a finite-difference method for diffusion and a vortex-in-cell method for convection and stretching. Numerical results are presented for an ellipsoid of axis ratio 2:1 and the limiting case of a sphere at various Reynolds numbers between 100 and 3000. Special consideration is given to the evaluation of the drag coefficient which is computed with three different approaches, denoted by S, P and V respectively. Particular emphasis is placed on the numerical implications and physical significance of each of these different approaches. Comparisons between numerical and analytical results at small times show very close agreement in each case. Separation angles, wake lengths and stationary drag coefficients for the sphere are also found to be in good agreement with previous results by a finite-difference method and with the standard drag curve.