A new implicit numerical treatment for non-linear turbulence models and its application to channels with spatially periodic corrugated walls

Abstract

This work examines the performance of linear and non-linear eddy-viscosity models when used to predict the turbulent flow in periodically sinusoidal-wave channels. Two geometries are investigated, namely a converging-diverging channel and a channel with concave-convex walls. The numerical method employed for the discretization of the equations is the control-volume method in a boundary-fitted non-orthogonal coordinate system. The SIMPLE algorithm is used for correcting the pressure field. The classical wall function and a low Reynolds model are used to describe the flow near the wall. Comparisons between those two approaches using linear and non-linear turbulence models are done. Here, an implicit numerical treatment was proposed for the non-linear diffusion terms of the momentum equations in order to increase the robustness of the solution method.