Low-Reynolds Number Turbulence Models: An Approach for Reducing Mesh Sensitivity

Abstract

This study presents a new near-wall treatment for low-Reynolds number (LRN) turbulence models that maintains accuracy in ‘coarse’ mesh predictions. The method is based on a thorough examination of approximations made when integrating the discretized equations in the near-wall region. A number of modifications are proposed that counteract errors introduced when an LRN-model is used on meshes for which the first interior node is located at y+≈5. Here the methodology is applied to the k−ω turbulence model by Bredberg et al., although similar corrections are relevant for all LRN models. The modified model gives asymptotically, in the sense of mesh refinement, identical results to the baseline model. For coarser meshes y+⩽10, the present method improves numerical stability with less mesh-dependency than the non-modified model. Results are included for fully developed channel flow, a backward-facing step flow and heat transfer in a periodic rib-roughened channel.