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Bogey and Bailly, 2010). The computational aspects involved in the modelling of such complex flows, typically, include the issues of high-resolution numerical schemes, boundary conditions, non-uniform grids and the choice of subgrid scale parameterization in case of LES modelling. Stepping back from this complexity to more idealised problems, two-dimensional (2D) vortex problems are a key object for testing different modelling strategies. Such reducedorder systems play an important role in the understanding of full-scale flow problems as well as in benchmarking of computational methods.

34 Advanced Fluid Dynamics (а) (b) (c) (d) (e) (f) (g) (h) Fig. 10. Vorticity distribution of leapfrogging vortices at several consecutive time moments: at /   0 (a), 18 (b), 36 (c), 54 (d), 72 (e), 90 (f), 108 (g), 120 (h). (a) (b) (c) Fig. 11. Vorticity distribution of the leapfrogging vortex pairs at at /   90 for (a) CABARET solution with the grid density of 6 cells per vortex core radius, (b) CABARET solution on the grid with 12 cells per vortex core radius, and (c) the reference vortex particle method solution from Eldridge (2007).

P ')  f ( R , ) of the computed solution at distance R=L from the vortex centre. Two grid resolutions are considered, 7 and 14 grid cells per acoustic wavelength. The polar angle variation corresponds to the top half of the computational domain which intersects one of the caustics bifurcation point at ~ 700 relative to the incident wave direction. s. solutions are computed with two grid densities, as shown in Figs 6c,d. It can be seen the main features such as the caustic point location and the peak amplitudes are well captured on both grids.

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