Christoph Reisinger, Markus Wabro,
"Analysis and Numerical Solution of the k-epsilon Turbulence Model with Non-Standard Boundary Conditions"
, 6-1999, C.Reisinger, M.Wabro: Analysis and Numerical Solution of the k-epsilon Turbulence Model with Non-Standard Boundary Conditions, diploma thesis, Institute of Analysis and Computational Mathematics, University Linz, 1999.
Original Titel:
Analysis and Numerical Solution of the k-epsilon Turbulence Model with Non-Standard Boundary Conditions
Sprache des Titels:
Englisch
Original Kurzfassung:
This thesis covers the entire solution procedure of the Navier-Stokes equations coupled with a common two-equation turbulence model, the $k$-$\epsilon$ model.
After a derivation of the model with a special emphasis on the boundary conditions derived from a boundary layer model at solid walls, positive answers to existence and uniqueness questions of the Navier-Stokes equations with turbulent eddy-viscosity (and coupled with a wall law) can be given under similar restrictions as known for pure Navier-Stokes equations with Dirichlet conditions. Various inflow and outflow conditions are studied.
The numerical solution procedure is based on a finite element discretisation of both the Navier-Stokes part and the $k$-$\epsilon$-system. A stabilising technique for the conforming $P_1$-$P_1$ element is used for the Navier-Stokes equations, the convection term is stabilised by the streamline diffusion method. For the $k$- and $\epsilon$-equations we employ a stable semi-implicit
multi-step scheme in combination with upwinding, in order to guarantee positivity of the solutions.
Sprache der Kurzfassung:
Englisch
Erscheinungsmonat:
6
Erscheinungsjahr:
1999
Notiz zum Zitat:
C.Reisinger, M.Wabro: Analysis and Numerical Solution of the k-epsilon Turbulence Model with Non-Standard Boundary Conditions, diploma thesis, Institute of Analysis and Computational Mathematics, University Linz, 1999.