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American Institute of Aeronautics and Astronautics

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    Course Outline

    Turbulence Modeling for CFD

    Course Outline:

    I. Introduction
    A. The ideal turbulence model, physics of turbulence, history of turbulence modeling

    II. The closure problem
    A. Reynolds averaging, Reynolds averaged equations, the Reynolds stress equation, length scales and their behavior, equations vs. unknowns

    III. Algebraic models
    A. Molecular transport of momentum, the mixing-length hypothesis
    B. How molecules and eddies are different
    C. Free shear flows
    D. Cebeci-Smith and Baldwin-Lomax models
    E. Channel/pipe flow
    F. Attached boundary layers
    G. Separated flows
    H. The half-equation model
    I. Range of applicability

    IV. One- and two-equation models
    A. The turbulence energy equation
    B. One-equation models, two-equation models/generic
    C. k-e and k-w models
    D. Closure coefficients
    E. Free shear flows
    F. Cross diffusion
    G. Sensitivity to freestream conditions
    H. Surface boundary conditions
    I. Channel/pipe flow
    J. Perturbation analysis of the boundary layer
    K. Attached boundary layers
    L. Low-Reynolds-number corrections
    M. Transition prediction
    N. Separated flows
    O. The stress-limiter concept
    P. Range of applicability

    V. Effects of compressibility
    A. Favre-averaging, Favre-averaged equations
    B. Compressible-flow closure approximations
    C. Dilatation dissipation
    D. Compressible mixing layer
    E. Compressible law of the wall
    F. Shock-induced separation
    G. Stress limiter revisited
    H. The reattachment-point heat-transfer anomaly

    VI. Beyond the Boussinesq Approximation
    A. Nonlinear constitutive relations
    B. Algebraic Stress Models
    C. Why the stress limiter works so well
    D. Second-order closure models
    E. Pressure-strain correlation modeling
    F. LRR and Wilcox stress-w models
    G. Free shear flows, channel/pipe flow
    H. Attached boundary layers
    I. Streamline curvature
    J. Rotating channel flow
    K. Unsteady boundary layers
    L. Separated flows
    M. Range of applicability

    VII. Numerical considerations
    A. Multiple time scales and stiffness
    B. Near wall solution accuracy
    C. Turbulent/nonturbulent interfaces
    D. Parabolic marching methods
    E. Elementary time-marching methods
    F. Block-implicit methods
    G. Iteration and grid convergence

    VIII. New horizons
    A. Direct numerical simulation
    B. Large-eddy simulation
    C. Detached-eddy simulation
    D. Chaos