Abstract
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.
Original language | English |
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Publication status | Published - Jun 1999 |
Fields of science
- 101 Mathematics
- 101014 Numerical mathematics
- 101016 Optimisation
- 101020 Technical mathematics
- 102009 Computer simulation
- 102022 Software development
- 102023 Supercomputing