Contents

 
• Introduction
• Some basic notations from tensor analysis
  • The metric tensor
  • The covariant derivative
  • The volume element
  • The divergence theorem in vector and tensor notation
• Discretization of the geometrical quantities
  • 2D-case
  • 3D-case
• Space discretization of the continuity and momentum equations
  • 2D-case
  • 3D-case
• Space discretization of the transport equation
  • Invariant finite volume discretization
  • Invariant discretization on non-smooth grids
  • Approximation methods for convective flux
  • Diffusion flux approximation
• Turbulence modeling and related numerical issues
  • Introduction
  • Two-equation eddy-viscosity models
  • Numerical aspects of two-equation eddy-viscosity modeling
    • Space discretization of the stress-strain model
    • Space discretization of the production term in two-equation models
    • 2D implementation of low-Reynolds-number modeling
    • Implementation of the positive scheme for two-equation models
• Implementation of the boundary conditions
  • Prescribed velocities
    • 2D implementation
    • 3D implementation
  • Stresses prescribed
    • 2D implementation
    • 3D implementation
  • Semi-natural outflow condition
    • 2D implementation
    • 3D implementation
  • Slip boundary condition
    • 2D implementation
    • 3D implementation
  • Transition of types of boundary conditions
    • 2D implementation
    • 3D implementation
  • Treatment of boundary conditions at the corners of the region
    • 2D
    • 3D
      • Edges
  • Boundary conditions for the transport equation
  • The wall function method
• Time-discretization
  • Introduction
  • The -method
  • The solution algorithm
• Pressure correction
  • Introduction
  • The pressure-correction method
• The linear solver
  • Introduction
  • Survey of iterative methods
  • Preconditioning
  • Concluding remarks
• Post-processing
  • Interpolation of scalars in 2D
  • Interpolation of the velocity in 2D
  • Computation of the stream function
• References
• Proof of () and ()
• Proof of () and ()