Non-linear eddy-viscosity models


Many flows in technical applications are turbulent. In order to simulate a turbulent flow in a short computing time, two-equation RANS turbulence models are used. The inherent lack of accuracy of such models is cured to some extent by expressing the modelled turbulent stresses as a non-linear function of local mean velocity gradients. In particular flows in rotating and/or complex geometries are more accurately simulated than with classical eddy-viscosity models (the standard k-epsilon model is the most famous one in this class).

Scope of research

Research has been done on two parts. On the one hand, an original non-linear expression for the turbulent stresses in terms of the mean local flow field was developed. On the other hand, the transport equation for epsilon, which is crucial with respect to the quality of the simulation results, has been improved. Both aspects lead to improved accuracy. The quality is considered satisfactory, so that for the moment (i.e. 2002) no more research is devoted to the further development of non-linear eddy-viscosity models.


  • Numerical Simulation and Modelling of Turbulent Combustion. B. Merci, PhD Thesis, Ghent University, Belgium (2000).
  • Non-linear, low-Reynolds two-equation Turbulence Models, S.Pattijn, PhD Thesis, Ghent University, Belgium (1999).
  • Computational Treatment of Source Terms in Two-Equation Turbulence Models Merci, B., Steelant, J., Vierendeels, J., Riemslagh, K. and Dick, E., AIAA Journal, Vol. 38(11), p. 2085-2093 (2000).
  • A Quasi-Realizable Cubic Low-Reynolds Eddy-Viscosity Turbulence Model with a New Dissipation Rate Equation Merci, B., De Langhe, C., Vierendeels, J. and Dick, E., Flow, Turbulence and Combustion, Vol. 66(2), p. 133-157 (2001).
  • Application of a New Cubic Turbulence Model to Piloted and Bluff-Body Diffusion Flames Merci, B., Dick, E., Vierendeels, J., Roekaerts, D.and Peeters, T.W.J., Combustion and Flame, Vol. 126(1-2), p. 1533-1556 (2001).