Geodesic
Simulation and visualization of formation of vortex ring, its propagation and transportation of passive scalar
Numerical methods and programming, Tome 22 (2021) no. 3, pp. 183-200.

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Numerical simulation of gas-dynamic processes accompanying the formation and propagation of vortex rings obtained using a piston generator is considered. The influence of the characteristics of the vortex ring on the transfer of the passive particles is discussed. Unsteady Navier–Stokes equations are used for numerical calculations, and finite volume method is applied to their discretization. The results of numerical simulation make it possible to obtain the geometric and dynamic characteristics of the vortex ring, which correspond to the self-similar theory of the vortex ring and experimental data. In addition to traditional approaches to visualization of vortex flows based on the construction of contours of various flow quantities, invariants of the velocity gradient tensor and the method of Lyapunov exponents over a finite time interval are used to visualize vortex structures.
Keywords: computational fluid dynamics, vortex dynamics, vortex ring, vorticity, finite Lyapunov exponent method. 
@article{VMP_2021_22_3_a0,
     author = {K. N. Volkov and V. N. Emelyanov and I. E. Kapranov},
     title = {Simulation and visualization of formation of vortex ring, its propagation and transportation of passive scalar},
     journal = {Numerical methods and programming},
     pages = {183--200},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2021_22_3_a0/}
}
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K. N. Volkov; V. N. Emelyanov; I. E. Kapranov. Simulation and visualization of formation of vortex ring, its propagation and transportation of passive scalar. Numerical methods and programming, Tome 22 (2021) no. 3, pp. 183-200. http://geodesic.mathdoc.fr/item/VMP_2021_22_3_a0/