An immersed-boundary finite volume method for simulations of flow in complex geometries.

*(English)*Zbl 1057.76039Summary: A new immersed-boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source/sink as well as a momentum forcing. The method is based on a finite volume approach on a staggered mesh together with a fractional-step method. Both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no-slip boundary condition on the immersed boundary, and also to satisfy the continuity for the cell containing the immersed boundary. In the immersed-boundary method, the choice of an accurate interpolation scheme satisfying the no-slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary. Therefore, we propose a stable second-order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body. Three different flow problems (decaying vortices and flows over a cylinder and a sphere) are simulated using the immersed-boundary method, and the results agree well with previous numerical and experimental results.

##### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

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

##### Keywords:

second-order interpolation
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\textit{J. Kim} et al., J. Comput. Phys. 171, No. 1, 132--150 (2001; Zbl 1057.76039)

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##### References:

[1] | Peskin, C.S., The fluid dynamics of heart valves: experimental, theoretical, and computational methods, Annu. rev. fluid mech., 14, 235, (1982) |

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

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

[4] | J. Mohd-Yusof, Combined Immersed-Boundary/B-Spline Methods for Simulations of Flow in Complex Geometries, Annual Research Briefs (Center for Turbulence Research, NASA Ames and Stanford University, 1997, p, 317. |

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

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

[7] | Akselvoll, K.; Moin, P., Large eddy simulation of turbulent confined coannular jets and turbulent flow over a backward facing step, (1995) |

[8] | Kim, J.; Moin, P., Application of a fractional-step method to incompressible navier – stokes equations, J. comput. phys., 59, 308, (1985) · Zbl 0582.76038 |

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

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

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

[12] | Fornberg, B., Steady viscous flow past a sphere at high Reynolds numbers, J. fluid mech., 190, 471, (1988) |

[13] | Johnson, T.A.; Patel, V.C., Flow past a sphere up to a Reynolds number of 300, J. fluid mech., 378, 19, (1999) |

[14] | Constantinescu, G.S.; Squires, K.D., LES and DES investigations of turbulent flow over a sphere, (2000) · Zbl 1113.76354 |

[15] | Sakamoto, H.; Haniu, H., A study on vortex shedding from spheres in a uniform flow, J. fluid eng., 112, 386, (1990) |

[16] | Johnson, T.A., Numerical and experimental investigation of flow past a sphere up to a Reynolds number of 300, (1996), University of Iowa |

[17] | Jeong, J.; Hussain, F., On the identification of a vortex, J. fluid mech., 285, 69, (1995) · Zbl 0847.76007 |

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