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.
Highlights
The study of the flow field in case of an axisymmetric incompressible viscous fluid by using stochastic approach will be presented
In that paper the vortex blobs method has been applied to description of an axisymmetric viscous flow
The main idea of that is to approximate the vorticity by a large set of small vortex creatures called vortex blobs being transported in velocity field and performing random walks according to Wiener process
Summary
The study of the flow field in case of an axisymmetric incompressible viscous fluid by using stochastic approach will be presented. In that paper the vortex blobs method has been applied to description of an axisymmetric viscous flow They presented the stochastic interpretation of the vorticity equation which leads to the Ito differential equations determining the movement of large numbers of the blobs. The velocity field contains a proper potential component This component allows formulating boundary integral equation for the vorticity created at the moment. In an axisymmetric viscous flow, this method requires to study the mathematical and computational formulations of the problem This enables us to study the construction of axisymmetric vorticity carrier and find the solution of potential velocity field. The complete details and final results of this problem will be formulated and discuss in paper
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