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Numerical Simulation of N-S equations in Cylindrical Coordinate

Numerical Simulation of N-S equations in Cylindrical Coordinate. Kyongmin Yeo. Chung & Sung 2005. Marcus & Lee 1998. Introduction. Flows in Annular pipe Basic Instability pattern in geophysical flows Engineering Application Centrifugal Instability Couette flow

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Numerical Simulation of N-S equations in Cylindrical Coordinate

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

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

  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. cpu 1 2 3 … cpu 1 2 3 … 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

  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!

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