Direct Numerical Simulations using Vortex Methods
Direct numerical simulations are presented for viscous incompressible flows with and without solid wall boundaries. Our numerical method is based on vortex methods. The classical scheme is enhanced to account for viscous effects (diffusion and no-slip boundary condition) by appropriately modifying the strength of the particles. Computations for extended times are feasible by periodically remeshing the vorticity field. The particles are advanced using the Biot-Savart law for the evaluation of the velocity. Large scale computations using O(106) particles are feasible by efficiently employing fast summation algorithms. We present viscous and inviscid simulations of vortex merging and compare our results with those of spectral methods and contour dynamics. The impulsively started flow around a circular cylinder is also examined for Re = 40 to 9500.
KeywordsCircular Cylinder Direct Numerical Simulation Bluff Body Vorticity Field Vortex Sheet
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