| dc.contributor.advisor | Lube, Gert Prof. Dr. | |
| dc.contributor.author | Schroeder, Philipp W. | |
| dc.date.accessioned | 2019-03-07T09:06:16Z | |
| dc.date.available | 2019-03-07T09:06:16Z | |
| dc.date.issued | 2019-03-07 | |
| dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-002E-E5BC-8 | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-7330 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | Robustness of High-Order Divergence-Free Finite Element Methods for Incompressible Computational Fluid Dynamics | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Lube, Gert Prof. Dr. | |
| dc.date.examination | 2019-03-01 | |
| dc.description.abstracteng | In 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 efficiency. | de |
| dc.contributor.coReferee | Dillmann, Andreas Prof. Dr. | |
| dc.contributor.thirdReferee | Rebholz, Leo G. Prof. Dr. | |
| dc.subject.eng | computational fluid dynamics | de |
| dc.subject.eng | incompressible Navier-Stokes equations | de |
| dc.subject.eng | exactly divergence-free methods | de |
| dc.subject.eng | H(div)-DG and HDG methods | de |
| dc.subject.eng | structure preservation | de |
| dc.subject.eng | Helmholtz decomposition | de |
| dc.subject.eng | pressure- and Reynolds-semi-robustness | de |
| dc.subject.eng | laminar and turbulent flows | de |
| dc.subject.eng | Taylor-Green vortex | de |
| dc.subject.eng | turbulent channel flow | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-002E-E5BC-8-3 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematik (PPN61756535X) | de |
| dc.identifier.ppn | 167351894X | |