Singular Approximations for Calculating Vortex Filaments
V. L. Okulov1,2,3, Ya. Fukumoto4
1Kutateladze Institute of Thermophysics, SB RAS, Novosibirsk, 630090, Russia
2Technical University of Denmark, Nils Koppels Alle, 403, Lyngby, 2800, Denmark
3Novosibirsk State University, Novosibirsk, 630090, Russia
4Institute of Mathematics for Industry, Kyushu University, Fukuoka, 819-0395, Japan
Keywords: vortex dynamics, helical vortex, vortex filaments, desingularization, regularization of numerical solutions
Abstract
The accuracy of numerical calculations of the dynamics of vortex filaments is estimated via the truncation method using the example of the motion of helical vortices. In the case of helical vortices with uniform vorticity distribution in Rankine core, there are two more analytical approaches to solving the problem. These approaches are used to determine the minimum admissible distance between vortex filaments or their elements to ensure the accuracy of calculations when using the truncation method. There is an established error that occurs in the calculations based on the truncation method in the case of convergence of the windings of a helical vortex.
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