A face-centred finite volume method for laminar and turbulent incompressible flows

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 insensitive to mesh quality, 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.