κ-ω Turbulence model for the solution of 2-D internal flows by the FEM

This work presents validation of a k-ω turbulence model for the solution of two-dimensional, internal incompressible flows, using a formulation for compressible flows. The two turbulence equations are decoupled from the mean flow system and are solved in a segregated fashion by a Galerkin finite element method and a direct matrix solver. This solution procedure proves to be robust for the test cases performed in this work. The general characteristics of the model are illustrated through four test problems : a fully-developed channel flow for which smooth-wall and rough-wall boundary conditions for ω are tested, a developing pipe flow using a wall function approach, a developing Couette-Poiseuille flow and a backward facing step.