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

Masahisa Tabata

    Research output: Contribution to journalArticle

    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 languageEnglish
    Pages (from-to)129-138
    Number of pages10
    JournalModeling and Simulation in Science, Engineering and Technology
    DOIs
    Publication statusPublished - 2016

    Fingerprint

    Lagrange
    Galerkin
    Bubble
    Flow of fluids
    Numerical Simulation
    Fluids
    Fluid Flow
    Computer simulation
    Galerkin methods
    Energy
    Navier Stokes equations
    Interfaces (computer)
    Surface tension
    Lagrange Method
    Fluid
    Reynolds number
    Galerkin Method
    Surface Tension
    Smoothness
    Navier-Stokes Equations

    ASJC Scopus subject areas

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

    Cite this

    @article{b833adba1afc455f9a480ecb21fde58b,
    title = "Numerical simulation of the behavior of a rising bubble by an energy-stable Lagrange-Galerkin Scheme",
    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.",
    author = "Masahisa Tabata",
    year = "2016",
    doi = "10.1007/978-3-319-40827-9_10",
    language = "English",
    pages = "129--138",
    journal = "Modeling and Simulation in Science, Engineering and Technology",
    issn = "2164-3679",
    publisher = "Springer International Publishing AG",

    }

    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 -