coupled surface-subsurface flow modeling in gera software ...€¦ · Автоматическая...
TRANSCRIPT
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K. Novikov, INM RAS, Moscow, Russia
Coupled surface-subsurface flow modeling in GeRa software
package
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GeRa code
GeRa (Geomigration of Radionuclides) – software package designed for 3D hydrogeologic modeling to assess radioactive waste disposal safety
Nuclear Safety Institute of the Russian Academy of Sciences, Moscow
Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow
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Without surface runoff
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Without surface runoff
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Without surface runoff
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With surface runoff
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With surface runoff
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Without surface runoff
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With surface runoff
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Coupled model mesh
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Coupled model mesh
Surface runoff
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Coupled model mesh
Groundwater flow
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Surface runoff model
Diffusive wave approximation of shallow water equations:
5/3 5/3
| | | |s s s s s
sss s
h h H h H q qt x x y yH Hν ν
∂ ∂ ∂∂ ∂− − = − ∂ ∂ ∂ ∂ ∂∇ ∇
• hs – water depth • Hs = hs + z – water
elevation • q – sources/sinks
• qss – surface-subsurface flux
• v – Manning’s roughness coefficient
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Groundwater flow model
Modified Richards equation:
( )( )( ) 0g g
stor g g
h hSs K h z
t tθ∂ ∂
+ −∇⋅ ∇ + =∂ ∂
• θ – water content • hg – pressure head • S = S(hg) – saturation
• sstor – specific storage • Kg = K(hg) – hydraulic
conductivity
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Groundwater flow model Van Genuchten model:
• θ – water content • θr ,θs – residual and
maximum water content • α, n – medium parameters
• Ks – saturated conductivity • S – saturation • Se – effective saturation
for 0[1 | | ]( )
f 0 or
rr gn m
s
s
gg
g
hhh
h
θ θθαθθ
− + < += ≥
Mualem’s model:
10.5 2( ) · [1 (1 ) ] ,mm
es eK h K S S= − −
11mn
= −
re
s r
S θ θθ θ−
=−
s
S θθ
=
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Coupling of the models
if 0 otherwise
( )ssg g
q surfx aceK h
∈− ∇ =
5/3 5/3
| | | |s s s s s
sss s
h h H h H q qt x x y yH Hν ν
∂ ∂ ∂∂ ∂− − = − ∂ ∂ ∂ ∂ ∂∇ ∇
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Coupling of the models
( )ssss s g
Kq hd
h−=
• qss – surface-subsurface flux
• Kss – near-bottom sediment conductivity
• d – near-bottom sediment layer width
• hg – groundwater pressure head
• hs – surface water depth
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Coupling of the models
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Coupling of the models
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Coupling of the models
( )ssss s g
Kq hd
h−=
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Coupling of the models
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Coupling of the models
( )ssss s g
Kq hd
h−=
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Coupling of the models
( ) 0ssss s g
Kq h hd
−= >
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Coupling of the models
0ssq =
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Coupling of the models
( ) 0ssss s g
Kq h hd
−= <
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Coupling of the models
0 in A
( ) in
B,C,D
ssss s ghKq h
d
−=
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Surface runoff model discretization
5/3 5/3
| | | |s s s s s
sss s
h h H h H q qt x x y yH Hν ν
∂ ∂ ∂∂ ∂− − = − ∂ ∂ ∂ ∂ ∂∇ ∇
• hs – water depth • Hs = hs + z – water
elevation • q – sources/sinks
• qss – surface-subsurface flux
• v – Manning’s roughness coefficient
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Surface runoff model discretization
( ) ( )s ss s ss s s ss
h HK H q q K H q qt t
⇔∂ ∂
−∇ ∇ = − −∇ ∇ = −∂ ∂
• hs – water depth • Hs = hs + z – water
elevation • q – sources/sinks
• qss – surface-subsurface flux
• v – Manning’s roughness coefficient
5/3
| |s
ssH
K hν ∇
=
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Discretization of diffusion coefficient of surface runoff model (numerator)
5/3
| |s
ssH
K hν ∇
=
( )5/3
, ,5/3 5/3, 5/3
, ,
,
,
( ) , ,( )
( ) , .s i s i
s s ijs j
s j
ijs i
js
h H Hh
h Hh
H
≥= =
<
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Discretization of diffusion coefficient of surface runoff model (denomenator)
5/3
| |s
ssH
K hν ∇
=
, ,, , ( ( )) s j s j
s s j j jH HH H
yx
xy
x yα α α
∂ ∂+= + −
∂ ∂−
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Coupling of the models
0 in A
( ) in
B,C,D
ssss s ghKq h
d
−=
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Smoothing surface-subsurface flux
3 22
1(
0, (
) , (
,
, )2
( ), )
)
( ,
s
ss ss ssg s g
ss
s
s g
sss g s
s
g
hcosK K Kh h h h h Ad d
q BK h h h
d
dh C
h h
πεε
ε ε
−− ∈
= ∈
−
−
∈
−
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Numerical experiments
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Tilted v-catchment with subsurface
[S. Kollet et al. The integrated hydrologic model intercomparison project, ih-mip2: A second set of benchmark results to diagnose integrated hydrology and feedbacks // Water Resources Research 53 (1) (2017) 867-890]
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Tilted v-catchment with subsurface Parameter Value
Manning’s roughness channel, (h/m1/3) 1.74×10-3
Manning’s roughness banks, (h/m1/3) 1.74×10-4
Saturated hydraulic conductivity, (m/h) 10 Residual volumetric water content, (-) 0.08 Saturated volumetric water content, (-) 0.4
Precipitation rate, (m/h) Scenario I: 0;
Scenario II: 0.1 for 20 h, 0 afterwards
Van Genuchten parameter n, (-) 2 Van Genuchten parameter α, (m) 6 Experiment duration, (h) 120 Bottom sediment width, (m) 0.2 Bottom sediment conductivity, (m/day) 20
Initial conditions Water 2m below surface
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Tilted v-catchment with subsurface first scenario
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Tilted v-catchment with subsurface first scenario
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Tilted v-catchment with subsurface first scenario
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Tilted v-catchment with subsurface first scenario
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Tilted v-catchment with subsurface second scenario
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Tilted v-catchment with subsurface second scenario
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Tilted v-catchment with subsurface second scenario
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Tilted v-catchment with subsurface second scenario
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Borden experiment
[S. Kollet et al. The integrated hydrologic model intercomparison project, ih-mip2: A second set of benchmark results to diagnose integrated hydrology and feedbacks // Water Resources Research 53 (1) (2017) 867-890]
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Borden experiment Parameter Value
Manning’s roughness channel, (s/m1/3) 0.03
Manning’s roughness banks, (s/m1/3) 0.3
Saturated hydraulic conductivity, (m/h) 0.036 Residual volumetric water content, (-) 0.067 Saturated volumetric water content, (-) 0.37
Precipitation rate, (m/h) 0.02 first 50 minutes, 0 next 50 minutes
Van Genuchten parameter n, (-) 6 Van Genuchten parameter α, (m) 1.9 Experiment duration, (min) 100 Bottom sediment width, (m) 0.2 Bottom sediment conductivity, (m/day) 0.47 Initial conditions Water level 2.78m
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Borden experiment
[S. Kollet et al. The integrated hydrologic model intercomparison project, ih-mip2: A second set of benchmark results to diagnose integrated hydrology and feedbacks // Water Resources Research 53 (1) (2017) 867-890]
[Aquanty inc., HGS user manual. – Waterloo. – 2015.] [VanderKwaak J., Numerical simulation o flow and chemical transport in integrated surface-subsurface hydrologic systems, Ph.D. thesis, University of Waterloo, Waterloo, Ontario, Canada (1999)]
Manning’s roughness channel, (s/m1/3) 0.03
Manning’s roughness banks, (s/m1/3) 0.3
Manning’s roughness banks, (s/m1/3) 0.3
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Borden experiment
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Borden experiment
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Borden experiment
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Borden experiment
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Smith and Woolhiser
[R. Smith, D. Woolhiser, Overland Flow on an inltrating surface // Water Resources Research, 7 (4), (1971), 899-913.]
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Smith and Woolhiser Parameter Value
Manning’s roughness, (min/cm1/3) 0.000122
Saturated hydraulic conductivity, (cm/min) Layer 1: 0.184 Layer 2: 0.1452 Layer 3: 0.1296
Residual volumetric water content, (-) Layer 1: 0.05068 Layer 2: 0.05699 Layer 3: 0.05248
Saturated volumetric water content, (-) Layer 1: 0.3946 Layer 2: 0.4387 Layer 3: 0.4764
Precipitation rate, (m/h) 0.416667 first 15 min, 0 next 5 min
Van Genuchten parameter n, (-) Layer 1: 3.4265 Layer 2: 4.1371 Layer 3: 4.3565
Van Genuchten parameter α, (m) Layer 1: 0.07
Layer 2: 0.056 Layer 3: 0.0443
Experiment duration, (min) 20
Bottom sediment width, (m) 0.01
Bottom sediment conductivity, (m/day) 100
Initial conditions Saturation 0.2
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Smith and Woolhiser
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Summary • Surface runoff modelling allows more precise description
of precipitation • Diffusive wave approximation of shallow water equations
is used in GeRa package as a surface runoff model • Numerical experiments demonstrate good agreement of
GeRa with other packages