  This work presents the face-centred finite volume (FCFV) paradigm for the
simulation of compressible flows. The FCFV method defines the unknowns at the
face barycentre and uses a hybridisation procedure to eliminate all the degrees
of freedom inside the cells. In addition, Riemann solvers are defined
implicitly within the expressions of the numerical fluxes. The resulting
methodology provides first-order accurate approximations of the conservative
quantities, i.e. density, momentum and energy, as well as of the viscous stress
tensor and of the heat flux, without the need of any gradient reconstruction
procedure. Hence, the FCFV solver preserves the accuracy of the approximation
in presence of distorted and highly stretched cells, providing a solver
insensitive to mesh quality. In addition, FCFV is capable of constructing
non-oscillatory approximations of sharp discontinuities without resorting to
shock capturing or limiting techniques. For flows at low Mach number, the
method is robust and is capable of computing accurate solutions in the
incompressible limit without the need of introducing specific pressure
correction strategies. A set of 2D and 3D benchmarks of external flows is
presented to validate the methodology in different flow regimes, from inviscid
to viscous laminar flows, from transonic to subsonic incompressible flows,
demonstrating its potential to handle compressible flows in realistic
scenarios.
