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__A Lagrangian method for numerical analysis of distributed vortical dynamics__

V. Govorukhin

**Abstract**

The variant of vortex-in-cells method originally presented in [1, 3] is developed.
The equations are the geophysical models of the atmosphere in terms of stream function and vorticity. The method is based on vorticity approximation using its values in particles and the velocity finding by Galerkin method. Computed velocity is used for fluid particles trajectories calculation as ODE system solution.
The effectiveness of integrator is important for the solution of similar problems. The set of different integrators is studied on a number of test problems of particles dynamics. As a result the most suitable methods are suggested. The algorithm of adaptive choice of integrator based on fluid particles locations is offered.
The algorithm for studing the topological structure of vortex configurations and their structural stability is suggested. The effectiveness of numerical methods are illustrated by results of fluid dynamics problems investigation [2].

**Bibliography**

[1]
V.N. Govorukhin and K.I. Il'in,
Numerical study of an inviscid incompressible flow through a channel of finite length.
Int. J. Num. Methods Fluids 60, No. 12, 1315-1333 (2009).

[2]
V.N. Govorukhin, A.B. Morgulis and V.A. Vladimirov,
Planar inviscid flows in a channel of finite length: washout, trapping and self-oscillations of vorticity.
J. Fluid Mech. 659, 420-472 (2010).

[3]
V.N. Govorukhin,
A meshfree method for the analysis of planar flows of inviscid fluids.
LNCSE,V.89, pp. 171-180