Direct numerical simulations of unsteady separated flows using vortex methods

Citation

Koumoutsakos, Petros D. (1993) Direct numerical simulations of unsteady separated flows using vortex methods. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/TCQ9-9C86. https://resolver.caltech.edu/CaltechETD:etd-11122003-082957

Abstract

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Numerical simulations are presented for viscous incompressible flows with and without solid wall boundaries. Our numerical method is based on vortex methods. The classical inviscid scheme is enhanced to account for viscous effects via the method of particle strength exchange. The method is extended to account for the enforcement of the no-slip boundary condition as well by appropriately modifying the strength of the particles. Computations are possible for extended times by periodically remeshing the vorticity field.

The particles are advanced using the Blot-Savart law for the evaluation of the velocity. Computations are made using up to [...](10[superscript 6]) vortex particles by efficiently implementing the method of multipole expansions for vector computer architectures to obtain an [...](N) algorithm.

The method is used to simulate the inviscid evolution of an elliptical vortex in an unbounded fluid as well as unsteady separated flows around circular cylinders for a wide range of Reynolds numbers (40 - 9500). Direct comparisons are made of the results of the present method with those from a variety of theoretical, computational and experimental studies. The results exhibit the robustness and validity of the present method and allow to gain physical insight as to vorticity formation and its relation to the forces experienced by the body.

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