A circle theorem technique to handle 2-D flows around arbitrary cylinders in discrete vortex method

Discrete vortex method can effectively simulate the flow past an arbitrary body immersed in a two-dimensional, incompressible, viscous, infinite fluid. However, a common and insurmountable difficulty is encountered to deal with the vortex blobs leaking into the body. In this work, a novel boundary method is proposed to handle this issue, based on the circle theorem technique. Under this algorithm, the identical vortices are introduced outside the body to counteract the lost strengths of vortices through the use of the circle theorem and surface curvature. The novel method keeps the body surface streamlined and guarantees the total circulation to be conserved at each time step. A series of numerical simulations of flow over various cross-sectional bodies at high Reynolds numbers are performed to validate the accuracies in predicting the hydrodynamic loads, including flow past elliptic, foil, square, and triangular cylinders. Good agreements are obtained between the new technique predictions and experimental results.

Automated summary

The study introduces a novel boundary method to handle the leaking of vortex blobs by introducing identical vortices outside the body based on the circle theorem technique. This method maintains the streamlined body surface and conserves total circulation at each time step. Numerical simulations demonstrate good agreement between the new technique predictions and experimental results in predicting hydrodynamic loads.