VOF 法を用いた自由表面流れ解析における高精度解析 ?· vof 法を用いた自由表面流れ解析における高精度解析手法の構築…

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  • VOF

    1.

    1

    VOF(Volume of Fluid) 1)VOF

    VOF

    VOF

    VOF

    CIVA

    3

    2. (1)

    Navier-Stokes

    (uit

    + ujui,j fi) ij,j = 0 in (1)

    ui,i = 0 in (2)

    ui fi

    ij (3)

    ij = pij + (

    uixj

    +ujxi

    )(3)

    p (1)(2)

    SUPG/PSPG(Streamline Upwind Petrov

    Galerkin/Pressure Stabilizing Petrov Galerkin)

    2)P1/P1 1

    Crank-Nicolson

    Element-by-Element

    Bi-CGSTAB(2)

    1

    VOF1)VOF

    VOF 1 0

    0.5

    t+ ui,i = 0 in (4)

    ui

    VOF

    (5)

    = l + g(1 ), = l + g(1 ) (5)l, g, l, g

    (4) CIVA(Cubic

    Interporation with Volume/Area Coordinate)3)

    CIVA CIP 4) 3 4

    (6)

    VOF

    3

    (L1, L2, L3, L4) (7) 3

    n+1(x, y, z, t) = n(x ut, y vt, z wt, tt)(6)

    (L1, L2, L3, L4) =4

    i=1

    iLi+12

    4

    j,k=1(j 6=k)

    jkLjLk(1+LjLk)

    (7)

    , VOF

    i = i, jk = k j +3

    l=1

    (xlj xlk)kxl

    (8)

    (3)

    (0 < < 1) VOF

    (0 < < 1) (9)

    (10)

    D() = 1 + cos{2( 0.5)} (9)

    A(t) =

    D()dxdydz (10)

    D() 2

    0 (10)

    A(t) VOF err

    err =Verr(t)A(t)

    =(V (t) Vinit)

    A(t)(11)

    KeyWords VOFCIVA 112-8551 1-13-27 TEL 03-3817-1815 FAX 03-3817-1803

    58159

    -483-

    CS9-024

  • VVerr

    Vinit

    err

    err (12)

    VOF

    VOF

    err

    (t) = (t) 2err{

    0 < < 0.5, err > 00.5 < < 1, err < 0

    (12)

    2 (0 < < 1) 1/2

    (12)

    VOF 1 0

    1 10

    0

    VOF

    VOF-1

    VOF

    1 0

    f=0

    1

    0.5

    0

    (f )err

    2ferr

    2ferr

    f=1

    (f )err

    1

    3.

    -2 3

    (13)

    1m

    1m

    0.5m

    0.1m

    X

    Y

    Z

    50 5 50

    15606

    75000

    D =0.001t s

    A=9.3 10-3

    m

    w=5.311rad/s

    2

    f = A2 sin t (13)

    l = 998.0kg/m3, l = 1.01103Ns/m2g = 1.205kg/m3, g =

    1.81 105Ns/m2

    3.0[s] 6.0[s] 9.0[s] 3

    0 2 4 6 8 10

    0.4

    0.6

    0.8

    wat

    erle

    velo

    nle

    ftw

    all[

    m]

    time [s]

    4

    -3

    -4

    5) ALE

    6) 4305

    ALE

    4. VOF

    , 3

    CIVA

    3

    ALE

    1) C.W.Hirt and B.D.Nichols: Volume of Fluid (VOF)

    Method for the Dynamics of Free Boundaries, J. Comput.

    Phys., Vol.39, pp.201-2251981

    2) T.Tezduyar: Stabilized finite element formulations for

    incompressible flow computations, Advan. Appl. Mech.,

    Vol.28, pp.1-44, 1991

    3) N.Tanaka: The CIVA Method for Mesh-Free Approaches:

    Improvement of the CIP Method for n-Simplex, Comput.

    Fluid Dynamics J., Vol.8, no.1, pp121-127, 1999

    4) T.Yabe, T,Aoki: A universal solver for hyperbolic equa-

    tion by cubic-polynomial intrpolation. One-dimentional

    solver, Comput. Phys. Commun., 66, pp233-242, 1991

    5) :

    1992

    6) : PC ALE

    Vol.4, pp.113-120, 2001

    58159

    -484-

    CS9-024

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