Open AccessSTOCHASTIC VORTEX BLOBS METHOD TO STUDY AXISYMMETRIC FLOWS OF INCOMPRESSIBLE VISCOUS FLUID
Author(s) -
M. R. Hedar,
Ramy Kamel
Publication year - 2016
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v12i10.123
Subject(s) - mathematics , vortex , vorticity , rotational symmetry , compressibility , legendre polynomials , mathematical analysis , burgers vortex , boundary (topology) , classical mechanics , geometry , mechanics , physics
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.