A universal formulation of two-equation models for adaptive computation of turbulent flows Original Research Article

This paper describes the application of a recently developed universal adaptive finite element algorithm to the simulation of several turbulent flows. The objective of the present work is to show how the controlled accuracy of adaptive methods provides the means to perform careful quantitative comparisons of two-equation models. The formulation uses the logarithmic form of turbulence variables, which naturally leads to a simple algorithm applicable to all two-equation turbulence models. The new methodology is free of ad-hoc stability enhancement measures such as clipping and limiters which may often differ from one model to the other. Such techniques limit the predictive capability of a turbulence model and cloud the issues of a comparison study. The present procedure results in one adaptive solver applicable to all two-equation models. The approach is demonstrated by comparing three popular turbulence models on a few non-trivial compressible and incompressible flows. We have chosen the following models: the standard k−ϵ model, the k−τ model of Speziale and the k−ω model of Wilcox. Results show that accurate solutions can be obtained for all models, and that systematic comparison of turbulence models can be made.