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**A method of domain decomposition for calculating the steady flow past a cylinder.**
*(English)*
Zbl 0804.76025

Summary: For flow past a cylinder it is known that the vorticity is only significant in a thin boundary-layer adjacent to the surface and within a parabolic wake far from the cylinder. To address this behaviour of the vorticity, a numerical method is implemented whereby the flow field is decomposed into two regions: an inner region to deal with boundary-layer phenomena and an outer region to model wake phenomena. This method equally applies to any cylinder cross section. The equations of motion are solved in each region and matched at the boundary. Numerical solutions have been carried out for the trial case of a circular cylinder, and the agreement with existing results is good.

### MSC:

76D10 | Boundary-layer theory, separation and reattachment, higher-order effects |

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |

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\textit{S. J. D. D'Alessio} and \textit{S. C. R. Dennis}, J. Eng. Math. 28, No. 3, 227--240 (1994; Zbl 0804.76025)

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### References:

[1] | A. Thom, The flow past circular cylinders at low speeds. Proc. Roy. Soc. A 141 (1933) 651. · JFM 59.0765.01 |

[2] | M. Kawaguti, Numerical solution of the Navier-Stokes equations for flow around a circular cylinder at Reynolds numbers 40. J. Phys. Soc. Japan 8 (1953) 747. |

[3] | H.B. Keller and H. Takami, Numerical studies of viscous flow about cylinders. In: D. Greenspan (ed.), Numerical Solutions of Nonlinear Differential Equations. Wiley, New York (1966) p. 115. · Zbl 0173.18404 |

[4] | H. Takami and H.B. Keller, Steady two-dimensional viscous flow of an incompressible fluid past a circular cylinder. Phys. Fluids Suppl. II (1969) 51. · Zbl 0206.55004 |

[5] | S.C.R. Dennis and Gau-Zu Chang, Numerical integration of the Navier-Stokes equations in two-dimensions. Mathematics Research Center, University of Wisconsin. Technical Summary Report #859 (1969). |

[6] | S.C.R. Dennis and Gau-zau Chang, Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100. J. Fluid Mech. 42 (1970) 471. · Zbl 0193.26202 |

[7] | F. Nieuwstadt and H.B. Keller, Viscous flow past circular cylinders. Comp. Fluids 1 (1973) 59. · Zbl 0328.76022 |

[8] | S.C.R. Dennis, A numerical method for calculating steady flow past a cylinder. In: A.I. Van de Vooren and P.J. Zandbergen (eds), Proc. 5th Int. Conf. on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics 59 (1976) 165. · Zbl 0364.76018 |

[9] | B. Fornberg, A numerical study of steady viscous flow past a circular cylinder. J. Fluid Mech. 98 (1980) 819. · Zbl 0428.76032 |

[10] | P.J.S. Young, Steady asymmetric flow of a viscous fluid past a cylinder. Ph.D. Thesis, University of Western Ontario, London, Ontario, Canada (1989). |

[11] | I. Imai, On the asymptotic behaviour of viscous fluid flow at a great distance from a cylindrical body, with special reference to Filon’s Paradox. Proc. Roy. Soc. Lond. A208 (1951) 487. · Zbl 0043.19007 |

[12] | S.C.R. Dennis, A numerical method for calculating two-dimensional wakes. AGARD Conference Proceedings #60 on Numerical Methods for Viscous Flow (1967). |

[13] | S.C.R. Dennis, The numerical solution of the vorticity transport equation. In: H. Cabannes and R. Temam (eds), Proc. 3rd Int. Conf. on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics 19 (1973) 120. · Zbl 0264.76023 |

[14] | I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series and Products. 4th ed. Academic Press Inc., New York (1965). · Zbl 0918.65002 |

[15] | H.M. Badr, S.C.R. Dennis and P.J.S. Young, Steady and unsteady flow past a rotating circular cylinder at low Reynolds numbers. Comp. Fluids 17 (1989) 579. · Zbl 0673.76117 |

[16] | D.B. Ingham and T. Tang, A numerical investigation into the steady flow past a rotating circular cylinder at low and intermediate Reynolds numbers. J. Comp. Phys. 87 (1990) 91. · Zbl 0687.76037 |

[17] | S.J.D. D’Alessio and S.C.R. Dennis, A vorticity model for viscous flow past a cylinder. Comp. Fluids 23 (1994) 279. · Zbl 0802.76014 |

[18] | T. Tang and D.B. Ingham, On steady flow past a rotating circular cylinder at Reynolds numbers 60 and 100. Comp. Fluids 19 (1991) 217. · Zbl 0722.76089 |

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