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.

翻译：本研究首次开发了一种面向面心有限体积（FCFV）求解器，用于模拟层流与湍流粘性不可压缩流动。该公式基于雷诺平均纳维-斯托克斯（RANS）方程，并结合负Spalart-Allmaras（SA）湍流模型；此外，受黎曼求解器启发，推导了三种新型对流稳定化格式并进行了数值比较。所提方法实现了速度、速度梯度张量与压力的一阶收敛。FCFV方法能在非结构网格上精确预测工程关注量（如阻力与升力），并且通过避免梯度重构，即使存在高度畸变与拉伸的网格单元，该方法对网格质量的敏感性也低于其他有限体积方法。本文推导了RANS-SA系统的整体求解与交错求解策略，并进行了数值比较。通过包含层流与湍流、定常与非定常工况的数值基准算例，评估了所提FCFV方法的性能、精度与鲁棒性。