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

TL;DR

This paper introduces a divergence-free hybrid discontinuous Galerkin method for incompressible turbulent flows, offering advantages in physical accuracy and computational efficiency, and compares it with standard methods through numerical tests.

Contribution

It presents a novel H(div)-conforming hybrid discontinuous Galerkin discretization specifically designed for turbulent flow simulations, demonstrating its effectiveness and advantages over traditional methods.

Findings

The divergence-free method accurately captures turbulent flow structures.

The new discretization outperforms standard continuous Galerkin in certain cases.

Numerical validation confirms the method's efficiency and physical fidelity.

Abstract

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.