Finite element analysis of 2D turbulent flows using the logarithmic form of the k-? model

The logarithmic form for turbulent flow analysis guarantees the positivity of the turbulence variables as k and ? of the k-? model by using the natural logarithm of these variables. In the present study, the logarithmic form is incorporated into the finite element solution procedure for the unsteady turbulent flow analysis. A backward facing step flow using the standard k-? model and a flow around a 2D square cylinder using the modified k-? model (the Kato-Launder model) are simulated. These results show that the logarithmic form effectively keeps adequate balance of turbulence variables and makes the analysis stable during transient or unsteady processes.