On the implementation of the k − ε turbulence model in incompressible flow solvers based on a finite element discretization

A finite element implementation of the standard k − ε turbulence model including Chien’s Low-Reynolds number modification is presented. The incompressible Navier-Stokes equations are solved using an extension of the in-house software package FeatFlow (http://www.featflow.de). Algebraic flux correction based on a multidimensional flux limiter of TVD type (Kuzmin and Turek, 2004) is invoked to suppress nonphysical oscillations produced by the a priori unstable Galerkin discretization of convective terms. A block-iterative algorithm based on a hierarchy of nested loops is employed to advance the solution in time. Special emphasis is laid on the numerical treatment of wall boundary conditions. In particular, logarithmic wall functions are used to derive Neumann boundary conditions for the standard k − ε model. The resulting solutions are superior to those obtained using wall functions implemented as Dirichlet boundary conditions and comparable to simulation results produced by a Low-Reynolds number k − ε model. Two representative benchmark problems (channel flow and backward facing step) are used to compare the performance of different algorithms in 3D and to investigate the influence of the near-wall treatment.