Application of a near wall model to Navier-Stokes equations with nonlinear time-relaxation model

It is difficult and essential to determine appropriate boundary conditions for the flow averages because they depend on the behavior of the unknown flow near the wall. Large-eddy simulation (LES) is one of the promising approaches. LES estimates local spatial averages ū of the velocity u of the fluid. The main problem is modeling near-wall turbulence in complex geometries. Inspired by the works of Navier and Maxwell, the boundary conditions are developed on the wall. In this study, the appropriate friction coefficient for 2-D laminar flows is computed, and existing boundary layer theories are used to improve numerical boundary conditions for flow averages. The slip with friction and penetration with resistance boundary conditions are considered. Numerical tests on two-dimensional channel flow across a step using this boundary condition on the top and bottom wall and the step are performed.