TY  - GEN
N2  - 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.
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/26674/
A1  - Piatkowski, Stephan-Marian
ID  - heidok26674
KW  - Applied Mathematics
KW  -  Numerical Simulation
KW  -  Navier-Stokes Equations
KW  -  Environmental Sciences
TI  - A Spectral Discontinuous Galerkin method for incompressible flow
with Applications to turbulence
Y1  - 2019///
AV  - public
ER  -