Homogenization of a large eddy simulation model for turbulent fluid motion near a rough wall (Q1756631)

The paper under review deals with the numerical simulation of a turbulent viscous flow close to a periodic rough wall. More precisely, the authors consider the so-called large eddy simulation (LES) model and discuss the asymptotic behavior as the period \(\epsilon\) of the roughness tend to zero. Via homogenization, they find a critical scaling associated with the parameter \[ \lambda\equiv \lim_{\epsilon \to 0}\frac{a_\epsilon}{\epsilon^{5/3}}, \] where \(a_\epsilon\) is the amplitude of the roughness. For \(0<\lambda<\infty\) the roughness effect provides an additional nonlinear friction term which depends on an auxiliary nonlinear problem, which is solved by a numerical model based on a fixed point algorithm. Finally, they discuss the influence of the parameter \(\lambda\) for some geometrical settings.