Immersed boundary method for the incompressible Reynolds Averaged Navier–Stokes equations

This paper presents an immersed boundary method for the incompressible Reynolds Averaged Navier–Stokes equations using the k−ω−SST turbulence model and two different wall functions to approximate the near wall flow. The main focus of the paper is to address a range of numerical issues related to the implementation of the method and to describe in detail how to implement it in a finite volume code. The boundary conditions for the governing equations at the immersed boundary are imposed in a manner which is consistent with their treatment on a standard body conforming grid. The method is verified and validated by simulating a NACA 0012 airfoil at a Reynolds number of Re = 6⋅10⁶. The results confirm that the implementations are stable even on very coarse grids, however, in contrast to what is reported elsewhere in the literature, the predicted lift and drag of the airfoil are not necessarily improved by using a wall function which assumes a linear near wall velocity instead of a standard logarithmic velocity profile. Finally, the method is applied to the flow past a tree and shown to be able to make drag predictions, which are in good agreement with wind tunnel measurements.