A vortex method suitable for long time simulations of flow over body of arbitrary geometry

Abstract

In this paper, a core-spreading vortex method suitable for a long-time simulation of 2D flows over an immersed body of arbitrary shape is proposed. This vortex method employs the splitting and merging skills to control the convection error, imposes a vortex sheet on the body to enforce the no-slip boundary condition, selects a fast vortex method to speed up the computation, and finally takes advantage of the boundary element method to create the geometry flexibility. Several efforts have been made particularly in improving the long-time accuracy. Firstly, for the over-weak blobs generated during the blob splitting, we distribute their strength to nearby non-weak blobs through a near-to-far algorithm before removing them from the simulation. Secondly, we determine the appropriate approximation solution and optimize the discretization of the vortex sheet diffusion. Thirdly, to prevent blobs from staying too close to the wall, we define a proper near-wall region, which can be easily applied to arbitrarily shaped bodies, and exclude any blob from it. Finally, an outflow boundary condition is designed to control the total blob number. The flows induced by the impulsively started airfoil, circular, and elliptic cylinders are simulated and the accuracy and efficiency of the proposed vortex method are confirmed by the agreement of the present simulation results with those in the literatures.