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# Implementation of the Particle Strength Exchange Method for Fragmentons to Account for Viscosity in Vortex Element Method

 Authors: Kotsur O.S., Shcheglov G.A. Published: 08.06.2018 Published in issue: #3(78)/2018 DOI: 10.18698/1812-3368-2018-3-48-67 Category: Mathematics | Chapter: Computational Mathematics Keywords: vortex element method, particle strength exchange method, fragmentons, viscosity, vorticity, vorticity evolution equation

This paper focuses on the modification of the vortex element method for viscous incompressible flow simulations. Viscosity is accounted for using the Particle Strength Exchange (PSE) method by means of approximation of the viscous term in the vorticity evolution equation with an integral operator. Resolution equations for the parameters of the vortex elements (fragmentons) have been deduced: their marker position, direction and intensity. All the derivations are made by the assumption of noneffect of the vortex element additional vorticity. It has been shown that in the scope of this assumption, viscosity affects only the change of intensity of vortex elements. In such a case, in PSE method the elements follow trajectories of fluid particles, unlike in the Diffusive Velocity Method (DVM). Special focus is given to the discretization of initial vorticity onto the distributed system of vortex elements. Finally, the results of the diffusion problem of infinite vortex tube are described. Comparison of the numerical and analytical results confirms the correctness of the viscosity model for the considered problem

The study was supported by a grant from the Russian Foundation for Basic Research (project no. 17-08-01468 А)

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