  We present a novel high order semi-implicit hybrid finite volume/virtual
element numerical scheme for the solution of compressible flows on Voronoi
tessellations. The method relies on the flux splitting of the compressible
Navier-Stokes equations into three sub-systems: a convective sub-system solved
explicitly using a finite volume (FV) scheme, and the viscous and pressure
sub-systems which are discretized implicitly at the aid of a virtual element
method (VEM). Consequently, the time step restriction of the overall algorithm
depends only on the mean flow velocity and not on the fast pressure waves nor
on the viscous eigenvalues. As such, the proposed methodology is well suited
for the solution of low Mach number flows at all Reynolds numbers. Moreover,
the scheme is proven to be globally energy conserving so that shock capturing
properties are retrieved in high Mach number flows. To reach high order of
accuracy in time and space, an IMEX Runge-Kutta time stepping strategy is
employed together with high order spatial reconstructions in terms of CWENO
polynomials and virtual element space basis functions. The chosen
discretization techniques allow the use of general polygonal grids, a useful
tool when dealing with complex domain configurations. The new scheme is
carefully validated in both the incompressible limit and the high Mach number
regime through a large set of classical benchmarks for fluid dynamics,
assessing robustness and accuracy.
