Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method.

*(English)*Zbl 1061.76046Summary: A virtual boundary method is applied to the numerical simulation of a uniform flow over a cylinder. The force source term, added to the two-dimensional Navier-Stokes equations, guarantees the imposition of the no-slip boundary condition over the body-fluid interface. These equations are discretized, using the finite differences method. The immersed boundary is represented with a finite number of Lagrangian points, distributed over the solid–fluid interface. A Cartesian grid is used to solve the fluid flow equations. The key idea is to propose a method to calculate the interfacial force without ad hoc constants that should usually be adjusted for the type of flow and the type of the numerical method, when this kind of model is used. In the present work, this force is calculated using the Navier-Stokes equations applied to the Lagrangian points and then distributed over the Eulerian grid. The main advantage of this approach is that it enables calculation of this force field, even if the interface is moving or deforming. It is unnecessary to locate the Eulerian grid points near this immersed boundary. The lift and drag coefficients and the Strouhal number, calculated for an immersed cylinder, are compared with previous experimental and numerical results, for different Reynolds numbers.

##### MSC:

76M20 | Finite difference methods applied to problems in fluid mechanics |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

PDF
BibTeX
Cite

\textit{A. L. F. Lima e Silva} et al., J. Comput. Phys. 189, No. 2, 351--370 (2003; Zbl 1061.76046)

Full Text:
DOI

##### References:

[1] | Armfield, S.; Street, R., The fractional-step method for the navier – stokes equations on staggered grids: the accuracy of three variations, J. comp. phys., 153, 660, (1999) · Zbl 0965.76058 |

[2] | Dennis, S.C.R.; Chang, G., Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100, J. fluid mech., 42, 471, (1970) · Zbl 0193.26202 |

[3] | Fadlun, E.A.; Verzicco, R.; Orlandi, P.; Mohd-Yousof, J., Combined immersed-boundary finite-difference methods for three-dimensional complex flows simulations, J. comp. phys., 161, 35, (2000) · Zbl 0972.76073 |

[4] | Fogelson, A.L.; Peskin, C.S., A fast numerical method for solving three-dimensional Stokes equation in the presence of suspended particles, J. comp. phys., 79, 50, (1988) · Zbl 0652.76025 |

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

[6] | Goldstein, D.; Hadler, R.; Sirovich, L., Modeling a no-slip flow boundary with an external force field, J. comp. phys., 105, 354, (1993) · Zbl 0768.76049 |

[7] | Goldstein, D.; Hadler, R.; Sirovich, L., Direct numerical simulation of turbulent flow over a modelled riblet covered surface, J. comp. phys., 302, 333, (1995) · Zbl 0885.76074 |

[8] | D. Juric, Computation of phase change, Ph.D. Thesis, Mechanical Engineering, University of Michigan, USA, 1996 |

[9] | Kim, J.; Kim, D.; Choi, H., An immersed-boundary finite-volume method for simulations of flow in complex geometries, J. comp. phys., 171, 132, (2001) · Zbl 1057.76039 |

[10] | Lai, M.C.; Peskin, C.S., An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. comp. phys., 160, 705, (2000) · Zbl 0954.76066 |

[11] | R. Mittal, S. Balachandar, Inclusion of three-dimensional effects in simulations of two-dimensional bluff-body wake flows, ASME Fluids Engineering Division Summer Meeting, 1997 |

[12] | J. Mohd-Yusof, Combined immersed boundaries/B-splines methods for simulations of flows in complex geometries, CTR Annual Reserch Briefs, NASA Ames/Stanford University, 1997 |

[13] | Nishioka, M.; Sato, H., Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds numbers, J. fluid mech., 89, 49, (1978) |

[14] | Park, J.; Kwon, K.; Choi, H., Numerical solutions of flow past a circular cylinder at Reynolds number up to 160, KSME int. J., 12, 1200, (1998) |

[15] | Peskin, C.S., Numerical analysis of blood flow in the heart, J. comp. phys., 25, 220, (1977) · Zbl 0403.76100 |

[16] | Roshko, A., On the wake and drag of bluff bodies, J. aeronaut. sci., 22, 124, (1955) · Zbl 0064.20102 |

[17] | Sucker, D.; Brauer, H., Fluiddynamik bei der angestromten zilindern, Wärme stoffubertragung, 8, 149, (1975) |

[18] | Saiki, E.M.; Biringen, S., Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method, J. comp. phys., 123, 450, (1996) · Zbl 0848.76052 |

[19] | Schneider, G.E.; Zedan, M., A modified strongly implicit procedure for the numerical solution of field problems, Numer. heat transfer, 4, 1, (1981) |

[20] | Triton, D.J., Experiments on the flow past a circular cylinder at low Reynolds number, J. fluid mech., 6, 547, (1959) · Zbl 0092.19502 |

[21] | Wang, Q.; Squires, K.D., Int. J. multiphase flow, 22, (1996) · Zbl 1135.76577 |

[22] | White, F.M., Viscous fluid flow, (1991), McGraw-Hill New York |

[23] | Wieselsberger, C., New data on the laws of fluid resistance, Naca tn, 84, (1992) |

[24] | Williamson, C.H., Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds number, J. fluid mech., 206, 579, (1989) |

[25] | Williamson, C.H., Vortex dynamics in the cylinder wake, Ann. ver. fluid mech., 28, 477, (1996) |

[26] | Ye, T.; Mittal, R.; Udaykumar, H.S.; Shyy, W., An accurate Cartesian grid method for viscous incompressible flows with complex boundaries, J. comp. phys., 156, 209, (1999) · Zbl 0957.76043 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.