**6. Conclusion**

The computational of compressible vortical flows is challenging because of the multi-scale phenomena involved. Computational approaches and numerical methods for the solution of compressible vortical flow problems have been discussed. In particular, the key elements of a successful computational method have been outlined that include low numerical dissipation and low dispersion, as well as the good vortex preservation property. For the sake of illustration, several two-dimensional problems are considered that typically present a challenge for conventional Eulerian numerical schemes. The problems include the preservation of steady vortex in a box domain, acoustic wave scattering by a vortex field and the dynamics and acoustics of counter-rotating vortices pairs. For these problems, several computational solutions are presented and discussed, including those obtained with the CABARET scheme developed by the authors. Analytical and reference solutions are provided where applicable. All test problems considered are promoted as the benchmark problems for new Computational Fluid Dynamics codes that are to be used in application for hydrodynamics and acoustics of vortex resolving simulations.
