A Novel Variant of the K-ω URANS Model for Spectral Element Methods: Implementation, Verification, and Validation in Nek5000

Unsteady Reynolds-averaged Navier-Stokes (uRANS) models can provide good engineering estimates of wall shear and heat flux at a significantly lower computational cost compared with LES simulations. In this paper, we discuss the implementation of two novel variants of the k-ω turbulence model, the regularized k-ω standard and the regularized k-ω SST model, in a spectral element code, Nek5000. We present formulation for the specific dissipation rate (ω) in the standard k-ω model, which would obviate the need for ad hoc boundary conditions of ω on the wall. The regularized approach is designed to lead to grid-independent solutions as resolution is increased. We present a detailed comparison of these novel methods for various standard problems including the T-junction benchmark problem. The two approaches presented in this work compare very well with the standard k-ω model and experimental data for all the cases studied.