title: A Spectral Discontinuous Galerkin method for incompressible flow  with Applications to turbulence
creator: Piatkowski, Stephan-Marian
subject: ddc-004
subject: 004 Data processing Computer science
subject: ddc-500
subject: 500 Natural sciences and mathematics
subject: ddc-510
subject: 510 Mathematics
subject: ddc-530
subject: 530 Physics
description: In this thesis we develop a numerical solution method for the instationary incompressible  Navier-Stokes equations. The approach is based on projection methods for discretization in time and a  higher order discontinuous Galerkin discretization in space. We propose an upwind scheme for the  convective term that chooses the direction of flux across cell interfaces by the mean value of the  velocity and has favorable properties in the context of DG. We present new variants of solenoidal  projection operators in the Helmholtz decomposition which are indeed discrete projection  operators. The discretization is accomplished on quadrilateral or hexahedral meshes where  sum-factorization in tensor product finite elements can be exploited. Sum-factorization  significantly reduces algorithmic complexity during assembling. In this thesis we thereby build  efficient scalable matrix-free solvers and preconditioners to tackle the arising subproblems in the  discretization. Conservation properties of the numerical method are demonstrated for both problems  with exact solution and turbulent flows. Finally, the presented DG solver enables long time stable  direct numerical simulations of the Navier-Stokes equations. As an application we perform  computations on a model of the atmospheric boundary layer and demonstrate the existence of surface  renewal.
date: 2019
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/26674/1/Piatkowski_Dissertation.pdf
identifier: DOI:10.11588/heidok.00026674
identifier: urn:nbn:de:bsz:16-heidok-266746
identifier:   Piatkowski, Stephan-Marian  (2019) A Spectral Discontinuous Galerkin method for incompressible flow with Applications to turbulence.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/26674/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng