Turbulence Modeling

Week 1: Introduction to turbulence theory, statistical analysis (random process, ensemble mean, variance, single- and multi-point statistics, spatial and temporal correlation)

Week 2:Cartesian tensors, governing equations of fluid motion, Reynolds averaged Navier-Stokes (RANS) equations, turbulence closure problem

Week 3:Equation for fluctuating fluid motion, Reynolds stress transport equation, statistical stationarity and statistical homogeneity

Week 4:Turbulence kinetic energy equation; turbulence characteristics: diffusive, dissipative and redistribution; mean kinetic energy equation and turbulence production

Week 5:Turbulent boundary layer: outer layer and inner layer, inertial and viscous sub-layers, inner scaling

Week 6:RANS modeling: Boussinesq approximation, eddy-viscosity, zero-equation modeling, two-equation modeling, standard k-ε model, model constants

Week 7:RNG k-ε model, one-equation modeling, k-ω models, wall-functions

Week 8:Low-Reynolds number (LRN) models, ε boundary conditions, Initial conditions

Week 9:Realizability constraints, Reynolds stress models (RSM): pressure strain-rate modeling (slow and rapid parts), wall-correction, algebraic stress models

Week 10:Direct numerical simulation (DNS), Kolmogorov hypothesis, large eddy simulation (LES): resolved and sub-grid scales, filtered Navier-Stokes equations

Week 11:Filter types, sub-grid scale (SGS) modeling: Smagorinsky model, one-equation kSGS model, dynamic Smagorinsky model

Week 12:Scale similarity models, grid convergence in LES, hybrid RANS-LES approach, detached eddy simulation (DES)