Numerical simulation of n s equations in cylindrical coordinate
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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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Presentation Transcript

Introduction l.jpg

Chung & Sung 2005 Coordinate

Marcus & Lee 1998

Introduction

  • Flows in Annular pipe

    • Basic Instability pattern in

      geophysical flows

    • Engineering Application

  • Centrifugal Instability

    • Couette flow

  • Flow around cylinder


Governing equation l.jpg
Governing Equation Coordinate

  • Continuity equation

  • Momentum equation


Spatial discretization l.jpg
Spatial Discretization Coordinate

  • Spectral Method in θ and z directions

  • Spectral Element Method in r direction



Temporal discretization nonlinear step l.jpg
Temporal Discretization: Nonlinear step Coordinate

  • Higher-order dual splitting scheme

  • Nonlinear step


Pressure step l.jpg
Pressure step Coordinate

  • Galerkin approximation


Pressure step8 l.jpg
Pressure Step Coordinate

  • Pressure boundary condition

  • Velocity correction


Viscous step l.jpg
Viscous step Coordinate

  • Galerkin approximation


Fourier transform l.jpg

cpu Coordinate

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


Computation mesh l.jpg
Computation Mesh Coordinate









Re 400 l.jpg
Re = 400 Coordinate


Oscillating wall l.jpg
Oscillating Wall Coordinate

Stokes Layer


Z vorticity at re 400 800 l.jpg
Z - Vorticity at CoordinateRe = 400 & 800


Flow around a cylinder l.jpg
Flow around a cylinder Coordinate

Stokes flow solution




Thank you l.jpg
Thank you! Coordinate