Show simple item record

Robustness of High-Order Divergence-Free Finite Element Methods for Incompressible Computational Fluid Dynamics

dc.contributor.advisorLube, Gert Prof. Dr.
dc.contributor.authorSchroeder, Philipp W.
dc.titleRobustness of High-Order Divergence-Free Finite Element Methods for Incompressible Computational Fluid Dynamicsde
dc.contributor.refereeLube, Gert Prof. Dr.
dc.description.abstractengIn computational fluid dynamics, obtaining exactly divergence-free approximations to the incompressible Navier-Stokes equations, by means of finite element methods, has actually not been particularly popular in the last decade. This observation is in contrast to the fact that H(div)-conforming finite elements indeed facilitate the flexible construction of such methods in most diverse applications. In this context, from the methodical side, Discontinuous Galerkin (DG) methods play a key role and, from the computational point of view, the concept of hybridisation can and is exploited heavily. The present work demonstrates and explains why exactly divergence-free H(div) methods, especially in under-resolved simulations, show an excellent performance in several laminar and turbulent test scenarios. For convection-dominated problems, the use of upwinding, which is naturally incorporated into DG methods, is evaluated and assessed.  Furthermore, a careful investigation of various numerical examples is provided; this includes, for example, a Kelvin-Helmholtz instability problem, 2D and 3D freely decaying turbulence and turbulent channel flows. Especially, it is shown that H(div) methods provide a framework for the robust simulation of turbulent flows for basically any Reynolds number. From a theoretical perspective, it is shown that exactly divergence-free methods allow the transfer of many crucial fluid dynamics properties directly to the discrete level.  In fact, they allow for a comparably straightforward numerical error analysis as well, and it turns out that this success is strongly related to the concepts of pressure- and Reynolds-semi-robustness. One important consequence of pressure-robustness is that the accuracy of the resulting velocity approximation is completely independent of the quality of the pressure approximation. Finally, the role of high-order methods is investigated which shows that in the considered examples, using a moderate order promises to deliver a good compromise between accuracy and
dc.contributor.coRefereeDillmann, Andreas Prof. Dr.
dc.contributor.thirdRefereeRebholz, Leo G. Prof. Dr.
dc.subject.engcomputational fluid dynamicsde
dc.subject.engincompressible Navier-Stokes equationsde
dc.subject.engexactly divergence-free methodsde
dc.subject.engH(div)-DG and HDG methodsde
dc.subject.engstructure preservationde
dc.subject.engHelmholtz decompositionde
dc.subject.engpressure- and Reynolds-semi-robustnessde
dc.subject.englaminar and turbulent flowsde
dc.subject.engTaylor-Green vortexde
dc.subject.engturbulent channel flowde
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematik (PPN61756535X)de

Files in this item


This item appears in the following Collection(s)

Show simple item record