A new VOF-based numerical scheme for the simulation of fluid flow with free surface. II. Application to the cavity filling and sloshing problems.

*(English)*Zbl 1143.76537Summary: Finite element analysis of fluid flow with moving free surface has been performed in 2-D and 3-D. The new VOF-based numerical algorithm that has been proposed by the present authors [Part I, ibid. 765–790 (2003; Zbl 1143.76536)] was applied to several 2-D and 3-D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2-D and 3-D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non-uniform grid systems and can be extended to 3-D free surface flow problems without additional efforts.

##### MSC:

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

76M10 | Finite element methods applied to problems in fluid mechanics |

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

##### Keywords:

free surface; volume of fluid (VOF) method; orientation vector; baby-cell; cavity filling problem; sloshing problem##### Citations:

Zbl 1143.76536
PDF
BibTeX
XML
Cite

\textit{M. S. Kim} et al., Int. J. Numer. Methods Fluids 42, No. 7, 791--812 (2003; Zbl 1143.76537)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Hirt, Journal of Computational Physics 39 pp 201– (1981) |

[2] | Kim, International Journal for Numerical Methods in Fluids 42 pp 765– (2003) |

[3] | Finite element study of fluid flow with moving free surface. Ph.D. Thesis, Seoul National University; 1998. |

[4] | Dhatt, International Journal for Numerical Methods in Engineering 30 pp 821– (1990) |

[5] | Chan, Applied Mathematical Modelling 15 pp 624– (1991) |

[6] | Minaie, Journal of Engineering Materials Technology 113 pp 296– (1991) |

[7] | Usmani, International Journal for Numerical Methods in Engineering 35 pp 787– (1992) |

[8] | Numerical simulation of mold filling processes. Ph.D. Thesis, Purdue University; 1993. |

[9] | Lewis, International Journal for Numerical Methods in Fluids 20 pp 493– (1995) |

[10] | Hetu, Numerical Heat Transfer Part A 36 pp 657– (1999) |

[11] | Gao, International Journal for Numerical Methods in Fluids 29 pp 877– (1999) |

[12] | Goldschmit, International Journal for Numerical Methods in Engineering 46 pp 1505– (1999) |

[13] | Gaston, International Journal for Numerical Methods in Fluids 34 pp 341– (2000) |

[14] | Swaminathan, Applied Mathematical Modelling 18 pp 101– (1994) |

[15] | Shin, International Journal of Heat and Fluid Flow 21 pp 197– (2000) |

[16] | Ramaswamy, International Journal for Numerical Methods in Fluids 6 pp 659– (1986) |

[17] | Okamoto, International Journal for Numerical Methods in Fluids 11 pp 453– (1990) |

[18] | Ramaswamy, International Journal for Numerical Methods in Fluids 7 pp 1053– (1987) |

[19] | Huerta, Computer Methods in Applied Mechanics and Engineering 69 pp 277– (1988) |

[20] | Partom, International Journal for Numerical Methods in Fluids 7 pp 535– (1987) · Zbl 0618.76011 |

[21] | Jun, PhysicoChemical Hydrodynamics 10 pp 625– (1988) |

[22] | RIPPLE: A computer program for incompressible flows with free surfaces. Los Alamos National Laboratory Report, LA-12007-MS. 1994. |

[23] | Boundary Layer Theory. McGraw-Hill: New York, 1979. |

[24] | Fluid Mechanics. McGraw-Hill: New York, 1988. |

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.