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)
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