# 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

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