A universal formulation of two-equation models for adaptive computation ofturbulent flows

This paper describes the application of a recently developed universal adap tive finite element algorithm to the simulation of several turbulent hows. The objective of the present work is to show how the controlled accuracy of adaptive methods provides the means to perform careful quantitative compar isons of two-equation models. The formulation uses the logarithmic form of turbulence variables, which naturally leads to a simple algorithm applicabl e 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 predict ive capability of a turbulence model and cloud the issues of a comparison s tudy. The present procedure results in one adaptive solver applicable to al l two-equation models. The approach is demonstrated by comparing three popu lar turbulence models on a few non-trivial compressible and incompressible hows. We have chosen the following: models: the standard k - epsilon model, the k - tau model of Speziale and the k - omega model of Wilcox. Results s how that accurate solutions can be obtained for all models, and that system atic comparison of turbulence models can be made. (C) 2000 Elsevier Science S.A. All rights reserved.