Second Order Core Spreading Vortex Method in Two-Dimensional Viscous Flows

The purpose of the present paper is to examine numerically the theoretical results given by the previous work, in which an integral equation of Fredholm type with respect to vorticity is derived from the Navier-Stokes equations. From this integral equation, we derive the first and second order approximation and carry out the numerical calculation for the Oseen type vorticity distribution to confirm the validity of the core spreading method in this paper. Numerical results show that the classical core spreading method, the first order approximation, is valid within some finite time and the difference from the second order approximation is very small. This result implies that Greengard's notice that the core spreading method converges to a system of equations different from the Navier-Stokes equations is not surely correct in sense of engineering applications of the core spreading method.