## Analysis of the K-epsilon turbulence modelAimed at applied mathematicians interested in the numerical simulation of turbulent flows. Centered around the k- model, it also deals with other models such as one equation models, subgrid scale models and Reynolds Stress models. Presents the k- method for turbulence in a language familiar to applied mathematicians, but has none of the technicalities of turbulence theory. |

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### Contents

Homogeneous Incompressible Turbulence | 17 |

Reynolds Hypothesis | 29 |

Mathematical analysis and approximation | 63 |

Copyright | |

9 other sections not shown

### Common terms and phrases

airfoil algebraic algorithm almost-periodic approximation assume average boundary conditions boundary layer chapter closure terms coefficient compressible computational domain constant convection defined denotes derivation diffusion dimensions direct simulation Dirichlet Dirichlet boundary conditions dissipation equation model ergodic Euler equations Figure filter finite element method flat plate fluid formula frame invariance function Galilean invariant given gradients grid heat flux homogeneous turbulence incompressible flows initial conditions integrals isotropic Jn Jn kinetic energy laminar linear system low Reynolds number Mach number matrix mean flow mesh mixing layer multiple scales expansion Navier-Stokes equations obtained positive pressure problem quasi-periodic functions regions Reynolds equations Reynolds hypothesis Reynolds stress models Reynolds stress tensor right hand side rotation Smagorinsky's solution solve solver space stress tensor SUPG theorem triangles turbulence model turbulent flow turbulent kinetic energy values variables vector velocity field wall law zero