  This thesis deals with the investigation of a H(div)-conforming hybrid
discontinuous Galerkin discretization for incompressible turbulent flows. The
discretization method provides many physical and solving-oriented properties,
which may be advantageous for resolving computationally intensive turbulent
structures. A standard continuous Galerkin discretization for the Navier-Stokes
equations with the well-known Taylor-Hood elements is also introduced in order
to provide a comparison. The four different main principles of simulating
turbulent flows are explained: the Reynolds-averaged Navier-Stokes simulation,
large eddy simulation, variational multiscale method and the direct numerical
simulation. The large eddy simulation and variational multiscale have shown
good promise in the computation of traditionally difficult turbulent cases.
This accuracy can be only surpassed by directly solving the Navier-Stokes
equations, but comes with excessively high computational costs. The very common
strategy is the Reynolds-average approach, since it is the most cost-effective.
Those modelling principles have been applied to the two discretization
techniques and validated through the basic plane channel flow test case. All
numerical tests have been conducted with the finite element library
Netgen/NGSolve.
