### Abstract

This two coordinate systems description has been studied for a linearized version of the Navier-Stokes equations obtained by assuming a fixed velocity field v(o) in the convection term. The first results ζ and ψ are qualitatively so similar to the final solutions known from literature, that an iteration process, suggested-by deriving a new velocity field v(1) from ϕ, can be expected to show rapid convergence.

Original language | English |
---|---|

Title of host publication | Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede |

Editors | Adriaan I. van de Vooren, Pieter J. Zandbergen |

Place of Publication | Berlin, Heidelberg |

Publisher | Springer |

Pages | 101-106 |

ISBN (Electronic) | 978-3-540-37548-7 |

ISBN (Print) | 978-3-540-08004-6 |

DOIs | |

Publication status | Published - 1976 |

Event | 5th International Conference on Numerical Methods in Fluid Dynamics, NMFD 1976 - Twente University, Enschede, Netherlands Duration: 28 Jun 1976 → 2 Jul 1976 Conference number: 5 |

### Publication series

Name | Lecture Notes in Physics |
---|---|

Publisher | Springer |

Volume | 59 |

ISSN (Print) | 0075-8450 |

ISSN (Electronic) | 1616-6361 |

### Conference

Conference | 5th International Conference on Numerical Methods in Fluid Dynamics, NMFD 1976 |
---|---|

Abbreviated title | NMFD |

Country | Netherlands |

City | Enschede |

Period | 28/06/76 → 2/07/76 |

### Fingerprint

### Keywords

- Convection term
- Polar system
- Vorticity equation
- Vorticity distribution
- Polar grid

### Cite this

*Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede*(pp. 101-106). (Lecture Notes in Physics; Vol. 59). Berlin, Heidelberg: Springer. https://doi.org/10.1007/3-540-08004-X_303

}

*Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede.*Lecture Notes in Physics, vol. 59, Springer, Berlin, Heidelberg, pp. 101-106, 5th International Conference on Numerical Methods in Fluid Dynamics, NMFD 1976, Enschede, Netherlands, 28/06/76. https://doi.org/10.1007/3-540-08004-X_303

**Two coordinate systems description of viscous flow past a circular cylinder.** / van Beckum, F.P.H.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Two coordinate systems description of viscous flow past a circular cylinder

AU - van Beckum, F.P.H.

PY - 1976

Y1 - 1976

N2 - Two dimensional steady viscous exterior flow is often treated as an elliptic problem within a finite region, bounded by a big circle. Solutions by means of Fourier expansions or discretisation on a polar grid will only give reliable results for low Reynolds numbers. In the present paper an example of a transformation is given, that maps the entire vorticity field onto a rectangle so that: (a) the vorticity equation can develop its parabolic character, (b) the wake in the far field comes out properly, and (c) the restriction to low Reynolds numbers is removed. For the elliptic stream-function equation the polar system is retained.This two coordinate systems description has been studied for a linearized version of the Navier-Stokes equations obtained by assuming a fixed velocity field v(o) in the convection term. The first results ζ and ψ are qualitatively so similar to the final solutions known from literature, that an iteration process, suggested-by deriving a new velocity field v(1) from ϕ, can be expected to show rapid convergence.

AB - Two dimensional steady viscous exterior flow is often treated as an elliptic problem within a finite region, bounded by a big circle. Solutions by means of Fourier expansions or discretisation on a polar grid will only give reliable results for low Reynolds numbers. In the present paper an example of a transformation is given, that maps the entire vorticity field onto a rectangle so that: (a) the vorticity equation can develop its parabolic character, (b) the wake in the far field comes out properly, and (c) the restriction to low Reynolds numbers is removed. For the elliptic stream-function equation the polar system is retained.This two coordinate systems description has been studied for a linearized version of the Navier-Stokes equations obtained by assuming a fixed velocity field v(o) in the convection term. The first results ζ and ψ are qualitatively so similar to the final solutions known from literature, that an iteration process, suggested-by deriving a new velocity field v(1) from ϕ, can be expected to show rapid convergence.

KW - Convection term

KW - Polar system

KW - Vorticity equation

KW - Vorticity distribution

KW - Polar grid

U2 - 10.1007/3-540-08004-X_303

DO - 10.1007/3-540-08004-X_303

M3 - Conference contribution

SN - 978-3-540-08004-6

T3 - Lecture Notes in Physics

SP - 101

EP - 106

BT - Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede

A2 - van de Vooren, Adriaan I.

A2 - Zandbergen, Pieter J.

PB - Springer

CY - Berlin, Heidelberg

ER -