Near-Wall Modification of Spalart-Allmaras Turbulence Model for Immersed Boundary Method

An improved immersed boundary method for turbulent flow simulation on Cartesian grids is proposed. To determine the appropriate boundary conditions, near-wall approximation of the mean-flow equation and the Spalart-Allmaras turbulence model is investigated. A modified near-wall velocity profile that is linear with respect to the distance from the wall and that can be resolved by a numerical scheme with second-order spatial accuracy is derived. As with the velocity profile, the eddy-viscosity profile is modified to maintain the balance of the shear stress. To obtain the modified profile as a numerical solution, the boundary condition for the tangential velocity and the damping function in the Spalart Allmaras turbulence model is modified. Verification studies defined in the NASA Turbulence Modeling Resource are conducted. In all cases, the results confirm that the modified immersed boundary method produces a more accurate prediction of skin friction than the original immersed boundary method and show a consistent trend of grid convergence.