1. Numerical Simulation of N-S equations in Cylindrical Coordinate
Kyongmin Yeo

2. Introduction Flows in Annular pipe Centrifugal Instability
Chung & Sung 2005
Flows in Annular pipe
Basic Instability pattern in
geophysical flows
Engineering Application
Centrifugal Instability
Couette flow
Flow around cylinder
Marcus & Lee 1998

3. Governing Equation
Continuity equation
Momentum equation

4. Spatial Discretization
Spectral Method in θ and z directions
Spectral Element Method in r direction

5. Discretized equations

6. Temporal Discretization: Nonlinear step
Higher-order dual splitting scheme
Nonlinear step

7. Pressure step
Galerkin approximation

8. Pressure Step
Pressure boundary condition
Velocity correction

9. Viscous step
Galerkin approximation

10. Fourier Transform 3/2 rule is used for dealiasing
2-dimensional backward transform
complex to complex transform in θ direction
complex to real transform in z-direction
cpu 1 2 3 …
cpu …

11. Computation Mesh

12. Centrifugal Couette Flow

13. Taylor-Couette Instability

14. Azimuthal Vorticity at Re=500

15. Azimuthal Vorticity

16. Azimuthal Vorticity at Re=1000

17. Azimuthal Vorticity

18. Couette flow with Moving wall

19. Re = 400

20. Oscillating Wall
Stokes Layer

21. Z - Vorticity at Re = 400 & 800

22. Flow around a cylinder
Stokes flow solution

23. Flow around a cylinder at Re = 10

24. Flow around a cylinder at Re = 200

25. Thank you!