Integral wall model for large eddy simulations of wall-bounded turbulent flows

A new approach for wall modeling in Large-Eddy-Simulations (LES) is proposed and tested in various applications. To properly include near-wall physics while preserving the basic economy of equilibrium-type wall models, we adopt the classical integral method of von Karman and Pohlhausen (VKP). A velocity profile with various parameters is proposed as an alternative to numerical integration of the boundary layer equations in the near-wall zone. The profile contains a viscous or roughness sublayer and a logarithmic layer with an additional linear term that can account for inertial and pressure gradient effects. Similar to the VKP method, the assumed velocity profile coefficients are determined from appropriate matching conditions and physical constraints. The proposed integral wall-modeled LES (iWMLES) method is tested in the context of a pseudo-spectral code for fully developed channel flow with a dynamic Lagrangian subgrid model as well as in a finite-difference LES code including the immersed boundary method and the dynamic Vreman eddy-viscosity model. Test cases include a fully developed half-channel at various Reynolds numbers, a fully developed channel flow with unresolved roughness, a standard developing turbulent boundary layer flows over smooth plates at various Reynolds numbers, over plates with unresolved roughness, and a case with resolved roughness elements consisting of an array of wall-mounted cubes. The comparisons with data show that the proposed iWMLES method provides accurate predictions of near-wall velocity profiles in LES while, similarly to equilibrium wall models, its cost remains independent of Reynolds number and is thus significantly lower compared to existing zonal or hybrid wall models. A sample application to flow over a surface with truncated cones (representing idealized barnacle-like roughness elements) is also presented, which illustrates effects of subgrid scale roughness when combined with resolved roughness elements.