Shmagunov O.A.  

On simulation of no-slip condition in the method of discrete vortices

When modeling vortex flows of an incompressible fluid, it is possible to use the method of discrete vortices (MDV), where the continuous vorticity field is approximated by a set of discrete vortex elements moving in the velocity field [1]. The vortex elements have a clear physical interpretation, they do not require the construction of grids and are automatically adaptive, since they concentrate in the regions of greatest interest and successfully describe the flows of a non-viscous fluid. The possibility of using MDV in simulating flows of a viscous fluid was considered in [2-4] using the examples of flows past bodies with sharp edges with the no-penetration condition at solid boundaries. However, the appearance of vorticity on smooth boundaries requires the no-slip condition to be met when MDV is realized, which substantially complicates the initially simple method. In this connection, approaches are considered that allow solving the problem by simple means.

1.Belotserkovsky S. M., Lifanov I .. Method of Discrete Vortices. CRC Press, USA, 1997.
2. Scobelev B. Yu., Shmagunov OA A new approach to the modeling of viscous diffusion in vortex element methods, In: Fluid Mechanics and Its Applications, vol.44 (ed. E.Krause and K. Gersten), Kluwer Academic Publishers, 1998, p.95-104.
3. Scobelev B. Yu., Shmagunov O.A. Principal difficulties of turbulence description by Navier-Stokes equations and vortex methods, Proceedings of The First International Conference on Vortex Methods, November 4-5, 1999, Kobe, Japan, p.23-30.
4. Shmagunov OA Modeling of jet flows of a viscous fluid by the method of discrete vortices. Applied Mechanics and Technical Physics, 2012, vol.53, N 1, p. 24-31.

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