### Abstract

We consider two-fluid flow problems,where each fluid is governed by the Navier-Stokes equations and the surface tension proportional to the curvature acts on the interface. The domain which each fluid occupies is unknown,and the interface moves with the velocity of the particle on it. We have developed an energy-stable Lagrange-Galerkin finite element scheme for the two-fluid flow problems. It maintains not only the advantages of Lagrange-Galerkin method of the robustness to high-Reynolds numbers and of the symmetry of the resultant matrix but also the property of energy-stability under the condition of the smoothness of the interface. Here we perform numerical simulation of the behavior of a rising bubble by the scheme.

Original language | English |
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Pages (from-to) | 129-138 |

Number of pages | 10 |

Journal | Modeling and Simulation in Science, Engineering and Technology |

DOIs | |

Publication status | Published - 2016 |

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### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Engineering(all)
- Computational Mathematics
- Modelling and Simulation

### Cite this

**Numerical simulation of the behavior of a rising bubble by an energy-stable Lagrange-Galerkin Scheme.** / Tabata, Masahisa.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Numerical simulation of the behavior of a rising bubble by an energy-stable Lagrange-Galerkin Scheme

AU - Tabata, Masahisa

PY - 2016

Y1 - 2016

N2 - We consider two-fluid flow problems,where each fluid is governed by the Navier-Stokes equations and the surface tension proportional to the curvature acts on the interface. The domain which each fluid occupies is unknown,and the interface moves with the velocity of the particle on it. We have developed an energy-stable Lagrange-Galerkin finite element scheme for the two-fluid flow problems. It maintains not only the advantages of Lagrange-Galerkin method of the robustness to high-Reynolds numbers and of the symmetry of the resultant matrix but also the property of energy-stability under the condition of the smoothness of the interface. Here we perform numerical simulation of the behavior of a rising bubble by the scheme.

AB - We consider two-fluid flow problems,where each fluid is governed by the Navier-Stokes equations and the surface tension proportional to the curvature acts on the interface. The domain which each fluid occupies is unknown,and the interface moves with the velocity of the particle on it. We have developed an energy-stable Lagrange-Galerkin finite element scheme for the two-fluid flow problems. It maintains not only the advantages of Lagrange-Galerkin method of the robustness to high-Reynolds numbers and of the symmetry of the resultant matrix but also the property of energy-stability under the condition of the smoothness of the interface. Here we perform numerical simulation of the behavior of a rising bubble by the scheme.

UR - http://www.scopus.com/inward/record.url?scp=84992437043&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84992437043&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-40827-9_10

DO - 10.1007/978-3-319-40827-9_10

M3 - Article

SP - 129

EP - 138

JO - Modeling and Simulation in Science, Engineering and Technology

JF - Modeling and Simulation in Science, Engineering and Technology

SN - 2164-3679

ER -