1. LES 2003.1.10

2. Continuity Equation

3. Residual Stress Residual Stress Tensor Anisotropic residual stress tensor Residual kinetic energy Filtered pressure Advection term : energy transfer

4. Smagorinsky model ( for simple flow ) Eddy viscosity type model (* Exclude Backscatter) Smargorinsky length scale Smargorinsky coefficient Filtered width Characteristic filtered rate of strain

5. Transport equation ( incompressible flow ) constant

6. Dimensionless transport equation Symmetric tensor

7. No! Back Scatter Large scale Small scale Forward scatter Back scatter Energy transfer

8. Fourier series = unlimited trigonometric series Y X Z Ky Kx Kz General SpaceK - Space Fourier Transform

9. 1 – D Fourier transform

10. 2 – D Fourier Transform Mathematical Formulation = Analogue equation Algebra Formulation = Digital ( Discrete ) Equation

11. 3 – D Fourier Transform Mathematical Formulation = Analogue equation Algebra Formulation = Digital ( Discrete ) Equation