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

Exactly Divergence-free Hybrid Discontinuous Galerkin Method for Incompressible Turbulent Flows