Global Weak Solutions¶for the Two-Dimensional Motion¶of Several Rigid Bodies¶in an Incompressible Viscous Fluid

2002 ◽  
Vol 161 (2) ◽  
pp. 113-147 ◽  
Author(s):  
Jorge Alonso San Martín ◽  
Victor Starovoitov ◽  
Marius Tucsnak
Keyword(s):  
Viscous Fluid ◽  
Weak Solutions ◽  
Rigid Bodies ◽  
Incompressible Viscous Fluid ◽  
Two Dimensional ◽  
Global Weak Solutions

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

2016 ◽  
Vol 12 (10) ◽  
pp. 6739-6750
Author(s):  
M. R Hedar ◽  
R. S Kamel
Keyword(s):  
Viscous Fluid ◽  
Legendre Polynomials ◽  
Vortex Method ◽  
Stochastic Equations ◽  
Velocity Fields ◽  
Boundary Integral ◽  
Incompressible Viscous Fluid ◽  
Two Dimensional ◽  
Complete Elliptic Integrals ◽  
Total Velocity

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.

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