## Abstract

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.

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 |
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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 |
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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 |
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Abbreviated title | NMFD |

Country | Netherlands |

City | Enschede |

Period | 28/06/76 → 2/07/76 |

## Keywords

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