Analysis and Numerical Solution of the k-epsilon Turbulence Model with Non-Standard Boundary Conditions

Christoph Reisinger, Markus Wabro

Research output: ThesisMaster's / Diploma thesis

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 languageEnglish
Publication statusPublished - Jun 1999

Fields of science

  • 101 Mathematics
  • 101014 Numerical mathematics
  • 101016 Optimisation
  • 101020 Technical mathematics
  • 102009 Computer simulation
  • 102022 Software development
  • 102023 Supercomputing

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