Improved convergence characteristics of two-equation turbulence models on unstructured grids

Second order upwind scheme discretization of Reynolds-averaged Navier-Stokes turbulence models may lack robustness, especially when using unstructured grids. Among several factors that can be traced as the reasons, preserving a monotonic solution plays a key role. A possible remedy is to smooth the variation of the turbulence model dependent variables. To that end, a square root transformation is applied to the dependent variables of a k-& turbulence model. The new additional source diffusion terms that emerge as a result of the transformation are fully retained. Therefore, the transformed model reproduces the baseline k-& model performance. Moreover, the transformed model greatly enhances the robustness and reliability of turbulent flow simulations on unstructured grids.