A finite element implementation of the standard k-epsilon 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 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-epsilon 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-epsilon 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.