Reynolds-Averaged Navier-Stokes (RANS)

RANS is the Reynolds-averaged form of the Navier-Stokes equations, obtained by decomposing each flow variable into a mean and a fluctuation and time-averaging, which leaves the unclosed Reynolds-stress term -rho times the average of u_i’ u_j’. A turbulence model such as k-epsilon, k-omega, or Menter SST supplies that closure, usually through an eddy viscosity. RANS resolves the mean viscous boundary layer and wake, so it gives frictional and viscous-pressure resistance, propeller-hull interaction, and maneuvering forces that potential methods miss. Unsteady RANS (URANS) adds time accuracy. It is the workhorse of ship CFD, cheaper than LES or DES but reliant on the chosen turbulence model.