  This work develops, for the first time, a face-centred finite volume (FCFV)
solver for the simulation of laminar and turbulent viscous incompressible
flows. The formulation relies on the Reynolds-averaged Navier-Stokes (RANS)
equations coupled with the negative Spalart-Allmaras (SA) model and three novel
convective stabilisations, inspired by Riemann solvers, are derived and
compared numerically. The resulting method achieves first-order convergence of
the velocity, the velocity-gradient tensor and the pressure. FCFV accurately
predicts engineering quantities of interest, such as drag and lift, on
unstructured meshes and, by avoiding gradient reconstruction, the method is
less sensitive to mesh quality than other FV methods, even in the presence of
highly distorted and stretched cells. A monolithic and a staggered solution
strategies for the RANS-SA system are derived and compared numerically.
Numerical benchmarks, involving laminar and turbulent, steady and transient
cases are used to assess the performance, accuracy and robustness of the
proposed FCFV method.
