## Abstract

Numerical techniques frequently used for the simulation of one bubble can be classified as interface tracking techniques and interface capturing techniques. Most of these techniques calculate both the flow around the bubble and the shape of the interface between the gas and the liquid with one code. In this paper, a rising axisymmetric bubble is simulated with an interface tracking technique that uses separate codes to determine the position of the gasliquid interface and to calculate the flow around the bubble. The grid converged results correspond well with the experimental data. The gasliquid interface is conceived as a zero-mass, zero-thickness structure whose position is determined by the liquid forces, a uniform gas pressure and surface tension. Iterations between the two codes are necessary to obtain the coupled solution of both problems and these iterations are stabilized with a fluidstructure interaction (FSI) algorithm. The flow around the bubble is calculated on a moving mesh in a reference frame that rises at the same speed as the bubble. The flow solver first updates the mesh throughout the liquid domain given a position of the gasliquid interface and then calculates the flow around the bubble. It is considered as a black box with the position of the gasliquid interface as input and the liquid forces on the interface as output. During the iterations, a reduced-order model of the flow solver is generated from the inputs and outputs of the solver. The solver that calculates the interface position uses this model to adapt the liquid forces on the gasliquid interface during the calculation of the interface position.

Original language | English (US) |
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Pages (from-to) | 2303-2310 |

Number of pages | 8 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 234 |

Issue number | 7 |

DOIs | |

State | Published - Aug 15 2010 |

### Bibliographical note

Funding Information:J. Degroote gratefully acknowledges a Ph.D. fellowship and a grant for a long stay abroad at the Massachusetts Institute of Technology of the Research Foundation–Flanders (FWO). P. Bruggeman gratefully acknowledges a Ph.D. fellowship of the Research Foundation–Flanders (FWO).

## Keywords

- Bubble
- Fluid-structure interaction
- Interface tracking
- Partitioned