Rho-Taek Jung Date Title
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<Environmental Fluid Modeling>
Rho-Taek Jung
Date Title
2 June MEC Ocean Model
Introduction, Hydrostatic Model, Full-3D Model,
Eddy Viscosity, Boundary Condition
9 June Exercise1: MEC Model Manual Description
Pre-Process and Execution of Computer
Simulation of Oceanic Flow
Home Work to All
7 July Exercise2: Presentation of Simulation Results
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Numerical Ocean Circulation Model
Global Scale
Local Scale
Modular Ocean Model
(MOM : GFDL)
Earth Simulator
Washington university
Princeton Ocean Model
(POM)
Marine Environmental Committee Model
(MEC Model)
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MEC Ocean Model(Introduction)
1. Free Code developed by MEC (Marine Environmental Committee, of which in SNAJ)2. Organized University University of Tokyo, Kyushu University, Osaka University, Osaka Prefecture University3. Request : Oceanic flow simulation around marine artifacts4. Hydrostatic Model + Full-3D Model for meso-scale for human or artifact scale5. Use the merit of two models6. Strong source and sink flow around artifacts are occurred (Density Current Generator)
マリノフォーラム 21 パンフレットより
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MEC Ocean Model(Equations)
Hydrostatic approximation, Boussinesq approximation
z
x
y
z=
z=-H
z
uw
y
uv
x
uu
t
u
z
uK
zy
u
x
uA
x
pfv MM 2
2
2
2
0
1
z
vw
y
vv
x
vu
t
v
z
vK
zy
v
x
vA
y
pfu MM 2
2
2
2
0
1
gz
p
1
0
0
z
w
y
v
x
u
(1)
(2)
(3)
(4)
z
ww
y
wv
x
wu
t
w
z
wK
zy
w
x
wA
z
pg MM 2
2
2
2
0
1
(1’)
)1(),(
OL
H
vu
w
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MEC Ocean Model(Boundary Condition)
0
wy
Hv
x
Hu
Bottom
),( yxHz 22
02 vuux 22
02 vuvy
Surface : flow particle keeps on it through all subsequent time w
yv
xu
t
),,( yxtz 22 VUVC aDy 22 VUUC aDx
(5)(6)
(7)(8)
Integrating (2) under (5) and (6)
HHvdz
yudz
xtIntegrating (1) from the sea surface
H
gdzpp 0
(9)
(10)
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MEC Ocean Model(Tracer Equation)
Temperature and Salinity
(12)
(11)
(13)
z
Sw
y
Sv
x
Su
t
S
z
SK
zy
S
x
SA CC 2
2
2
2
z
Tw
y
Tv
x
Tu
t
T
z
TK
zy
T
x
TA CC 2
2
2
2
Boundary Condition
0z
TK h 0
z
SK s
heath Qz
TK
salinitys Qz
SK
at bottom
at surface (14)
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MEC Ocean Model(Eddy viscosity, Eddy diffusivity)
Horizontal eddy viscosity and eddy diffusivity : The rule of Richardson’s 4/3 which relates on the grid spacing.
CM AA ,
3/4
00
D
D
A
A
M
M
3/4
00
D
D
A
A
C
C
D0 : reference grid space
Vertical eddy viscosity and eddy diffusivity : It can be represented by stratification function.
MRiK
KM
M
M 10
CRiK
KC
C
C 10
2
0
z
Uz
gRi
2.5,1, MM 3/10,5.0, CC
CM KK ,
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MEC Ocean Model(Numerical Scheme)
Mainly Euler-backward scheme,
Upwind scheme, Central scheme
,,vu TS ,
Process of Primitive variables solution
1. Calculation of (3)(4)(2)2. Calculation of (9)3. Calculation of at surface (7)4. Calculation of (10)5. Output
wvu ,,wp
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MEC Ocean Model(Full-3D: Numerical Solution)
Staggered arrangement Grid System
Cartesian Coordinate system
MAC method
Explicit method
Third order upwind scheme (Convection Term)
Second central scheme (Diffusion Term)
SOR(Poisson equation of pressure)
Turbulence Model( model, SGS model, horizontal and vertical eddy viscosity coefficient)
k
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MEC Ocean Model(Full-3D)
gu
0
2
0
uuwu tmv
p
t
2at mvwu (1
6)
(15)
Turbulence Model
1. Horizontal and vertical eddy diffusivity coefficient
2. SGS(SubgridScale) Model
3. model k
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MEC Ocean Model(Full-3D: Turbulence Model)
1. Horizontal and vertical eddy diffusivity coefficient
k
3/4xAKH rV RiKK 10
sSHTH RiDDD )1(0
2. SGS(SubgridScale) Model
2/12 2 ijijSSGS SSC
SC ijS Tuu 2
1smagolinsky constant width of filter =
3. model
kk
k Pkkt
k 2u
212 cPc
kt kk
k
u
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MEC Ocean Model(Combine with Full-3D: Turbulence Model)
kSGSH orKMAX ..,
kSGSV orKMAX ..,
Special treatment of eddy diffusivity around interface between hydrodynamic model and full-3d model
HD Full-3D HD
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MEC Ocean Model(Combine with Full-3D : Time Interaction)
TIME
HD
Full-3D
Variables(Velocity,Temp.,Sali.,Tide) are interpolated
①
②
③-1
②④
①‘
N(step) N+1(step)
③- n③- ・・・
TIME
Large dT
Small dT
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MEC Ocean Model(Full-3D: Numerical Solution)
Overview of Full-3D subroutines
Ipola flux interpolation from hydrostatic model region to full-3d region.
Turb calculation of eddy diffusivity by chosen one of turbulence model
Gridmv calculation of moving velocity at surface due to the change of tide
Bcvel,bctemp,bcsal boundary condition for velocity, temperature, and salinity
Temp calculation of transfer equation for temperature
Sal calculation of transfer equation for salinity
Convct calculation of convect term of momentum equation
Buoy calculation of buoyancy term of momentum equation
Vis calculation of viscous term of momentum equation
Pres calculation of pressure and renew the value of the velocity
Opt1 print out the calculation results
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MEC test Simulation(DCG in Gokasho Bay)
After 12 hours After 96hours
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MEC test Simulation(DCG in Yumeikai)
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MEC test Simulation(DCG in Yumeikai)