Algebraic non-equilibrium wall-stress modeling for large eddy simulation based on analytical integration of the thin boundary-layer equation

An algebraic nonequilibrium wall-stress model for large eddy simulation is discussed. The ordinary differential equation (ODE) derived from the thin-layer approximated momentum equation, including the temporal, convection, and pressure gradient terms, is considered to form the wall-stress model. Based on the concept of the analytical wall function (AWF) for Reynolds-averaged turbulence models, the profile of the subgrid scale (SGS) eddy viscosity inside the wall-adjacent cells is modeled as a two-segment piecewise linear variations. This simplification makes it possible to analytically integrate the ODE near the wall to algebraically give the wall shear stress as the wall boundary condition for the momentum equation. By applying such integration to the wall-normal velocity component, the methodology to avoid the log-layer mismatch is also presented. Coupled with the standard Smagorinsky model, the proposed SGS-AWF shows good performance in turbulent channel flows at Re-tau = 1000-5000 irrespective of the grid resolutions. This SGS-AWF is also confirmed to be superior to the traditional equilibrium wall-stress model in a turbulent backward-facing step flow.