STOCHASTIC VORTEX BLOBS METHOD TO STUDY AXISYMMETRIC FLOWS OF INCOMPRESSIBLE VISCOUS FLUID

Abstract

This paper presents the mathematical and computational formulations of the stochastic Vortex Blobs Method (VBM). It isshow that how the method can be used to cover axisymmetric flows of incompressible viscous fluid. Also, the initialboundary problem is solved by using the Lagrangian vortex method. This method seems to be an extension of the well known two dimensional vortex blob method. When applying and extending this method two steps are required. First, wehave to design an axisymmetric vorticity carrier by using the standard functions as complete elliptic integrals and Legendre polynomials. Second, it is necessary to formulate the appropriate Neumann problem and boundary integral equation to find the potential velocity fields. Both steps are used to describe and compute the total velocity field and formulate the Ito stochastic equations which describing the motion of vorticity carriers.