A novel numerical treatment of the near-wall regions in the k−ω class of RANS models

In this paper, we discuss a novel approach to modeling the near-wall region in the class of k−ω models. The proposed methodology obviates the need for ad hoc boundary conditions of ω on the wall as typically required in the k−ω model. The primary motivation of this work is to provide a formulation equivalent to the standard k−ω and k−ω SST models, but which at the same time overcomes their limitations in the context of their implementation in high-order methods. This is achieved by subtracting the asymptotically known singular behavior of ω at walls. Imposing a grid-dependent value of ω at walls in high-order codes is not straightforward as is demonstrated below and it causes instability as well as accuracy issues. The mathematical formulation of the two novel approaches, termed as the “regularized k−ω model” and the “regularized k−ω SST model”, is discussed in detail. A consistency and verification study for these two approaches is performed by proving that the regularized models recover the results of the standard models in various canonical problems, such as turbulent channel and pipe flows, and a systematic investigation of convergence, using both p- (polynomial order) as well as h- (grid) refinement is reported. Furthermore, comparisons highlighting the performance of the proposed methods in more complex configurations such as flow over a backward facing step and the turbulent mixing of fluid streams of different temperatures in a T-junction are also presented.