advances towards a multi-physics, multi-dimensional ......h = ns1 e=0 e = ns 1 e=0 (x l;x r) e be...
TRANSCRIPT
Advances towards a multi-physics, multi-dimensional discontinuous
Galerkin method for modeling hurricane storm surge induced flooding
in coastal watershedsPrapti Neupane
&
This material is based upon work supported by the National Science Foundation under Grant DMS - 1217071.
Motivation
Outline
2 Recap Modeling Framework Channel Networks
3 Recent Work Kinematic Wave Equation 2-D Overland Flow Shallow Water Region Tests for Coupling between Bay and Channel How about Flooding?
4 Future Work
Motivation
Motivation
Figure: Harris County Flood Control high water mark data for Harris and portions of Galveston County from hurricane Ike surge2.
P. Neupane Research Overview February 5th, 2016 2 / 35
Motivation
Motivation
There are multiple softwares that simulate hurricane storm surge like ADCIRC, SLOSH (Sea, Lake and Overland Surges from Hurricanes), P-Surge (Probabilistic Hurricane Storm Surge) etc.
There are multiple softwares that simulate rainfall runoff in watersheds like HEC-RAS, MIKE21, FLO-2D etc.
However, there is no software that simulates the effects of storm surge combined with rainfall.
Goal: Develop a simulation engine that couples rainfall with storm surge to simulate flooding in coastal watersheds
P. Neupane Research Overview February 5th, 2016 3 / 35
Recap
Outline
2 Recap Modeling Framework Channel Networks
3 Recent Work Kinematic Wave Equation 2-D Overland Flow Shallow Water Region Tests for Coupling between Bay and Channel How about Flooding?
4 Future Work
Recap Modeling Framework
Introduction
Watershed - A geographic extent that shares a common drainage point, often called a sink
Coastal watersheds - usually drain to a bay/ocean
Key components of coastal watershed hydrology - Overland flow/rainfall runoff, channel/river flow and coastal flow
Figure: An illustration of a coastal watershed that includes key components of watershed hydrology1
P. Neupane Research Overview February 5th, 2016 4 / 35
Recap Modeling Framework
1 Overland flow region → land that receives rainfall
2 Channels → networks of drainage channels and rivers that receive water from overland flow region and carry it to a drainage point X
May contain junctions of different channels X
3 Shallow water region → part of the coast and ocean to where all the water from the watershed drains X
Handled by DGSWEM - Discontinuous Galerkin Shallow Water Equations Model
P. Neupane Research Overview February 5th, 2016 5 / 35
Recap Modeling Framework
∂
Recap Channel Networks
(2)
s → curvilinear coordinate along the centerline of the channel A→ wet cross-section area (L2) Q = uA→ mean cross-sectional volumetric discharge (L3/T ) β → dimensionless momentum flux correction factor (between 1 and 1.06 for normal channels) qL → lateral inflow rate per until length of channel (L3/T/L)
P. Neupane Research Overview February 5th, 2016 7 / 35
Recap Channel Networks
(2)
S0 = ∂z ∂s → bed slope; z is the bathymetric depth (positive downwards)
Sf → friction slope estimated using the Manning friction relationship: Sf = n2Q|Q| A2H
4 3
I1 = ∫ d
0 (d − y)W dy → hydrostatic pressure term; W → width of the channel
I2 = ∫ d
P. Neupane Research Overview February 5th, 2016 7 / 35
Recap Channel Networks
Recap Channel Networks
Channels
Network of channels are decomposed into 1-D channels and 2-D junctions
2-D shallow water equations are solved in the junctions
Equations solved using a 2-stage Runge-Kutta discontinuous Galerkin method
Coupling of 1-D channels and 2-D junctions handled via the numerical flux
P. Neupane Research Overview February 5th, 2016 8 / 35
Recent Work
2 Recap Modeling Framework Channel Networks
3 Recent Work Kinematic Wave Equation 2-D Overland Flow Shallow Water Region Tests for Coupling between Bay and Channel How about Flooding?
4 Future Work
Recent Work
Recent Work Kinematic Wave Equation
Overland flow region
Think of overland flow as a uniform flow in a wide channel with rectangular cross-sections in the direction of the surface slope gradient
This implies a balance between the gravitational force S0 and the frictional force (Sf ) in the momentum equation of (2) resulting in:
u = n−1 √ S0H
Kinematic Wave Equation
∂x (F ) = qL (4)
where x is the coordinate in the direction of the surface slope, F = Hu and u is given by (3), and qL = R − I , where R is rainfall intensity and I is infiltration.
P. Neupane Research Overview February 5th, 2016 10 / 35
Recent Work Kinematic Wave Equation
Discontinuous Galerkin Finite Element Method
Given a domain = (a, b) let h = N−1 e=0
e = N−1 e=0
(xL, xR)e be the finite
element partition of into a set of non-overlapping elements e . Let Vh =
{ v ∈ L2() : v |e ∈ Pk (e) ∀ e ∈ h
} .
Multiply (4) by φ ∈ Vh, integrating over e , rearrange and approximate H by Hh ∈ Vh to get:∫ xR
xL
∂Hh
− Fφ|xR +
qLφ dx (5)
where F represents a numerical flux that is defined such that it is continuous across element boundaries. Take F to be the upwind flux, i.e. F = FL.
P. Neupane Research Overview February 5th, 2016 11 / 35
Recent Work Kinematic Wave Equation
Space-Time Representation
Let ψi be a set of basis functions for Pk (e).Then, over an element e :
Hh(x , t) = N∑
Hj (t)ψj (x) (6)
where Hj are the time-dependent coefficients of expansion of Hh in the ψj
basis. Differentiate the above equation in time and substitute it in the DG equation (5):∑
j
∂Hj
∂t
∫ xR
xL
+
Recent Work Kinematic Wave Equation
Space-Time Representation
Replace φ in (7) with each of the basis functions ψj to obtain the following system of ordinary differential equations:
Me d
+
Recent Work Kinematic Wave Equation
Runge–Kutta Discretization
Discretize the set of ODEs given in (8) using strong stability preserving (SSP) explicit 2-stage Runge–Kutta time stepping methods.
H1 = Ht + tL(Ht)
Ht+1 = 1
Recent Work Kinematic Wave Equation
Parking Lot 1
receives rainfall at an intensity of 2in./h
calculate the outflow rate at the end of the parking lot for 60 min
analytical solution given in Kazezylmaz-Alhan et al.3
0 10 20 30 40 50 60
time (m)
DG Solution
Analytic Solution
Figure: Plot of the numerical solution obtained using 400 elements to discretize the parking lot along with the analytical solution.
P. Neupane Research Overview February 5th, 2016 15 / 35
Recent Work Kinematic Wave Equation
Parking Lot 2
100 ft long with slope = 0.005
receives rainfall at an intensity of 2in./h for the first 3 min increased to 4 in./h for the second 3 min
calculate the outflow rate at the end of the parking lot for 20 min
semi-analytical solution obtained by superposition of the outflow rates for each individual period of the two-period storm3
0 5 10 15 20
time (m)
DG Solution
First Storm
Second Storm
Semi-analytic Solution
Figure: Numerical solution obtained using 150 elements to discretize the parking lot.
P. Neupane Research Overview February 5th, 2016 16 / 35
Recent Work 2-D Overland Flow
P. Neupane Research Overview February 5th, 2016 17 / 35
Recent Work 2-D Overland Flow
Algorithm to Route Kinematic Flow in a 2-D Region
Discretize overland flow region with triangular elements
The three edges of a triangle are the three possible flow directions
Pick the edge with the lowest elevation at the midpoint to be the flow edge
Each arrow in the diagram represents a kinematic element
On each kinematic element, solve the kinematic wave equation
Add the fluxes coming into an element if that element receives water from multiple elements
P. Neupane Research Overview February 5th, 2016 18 / 35
Recent Work 2-D Overland Flow
Connect Overland Flow Region with Channels
Channels receive flow from overland flow region as lateral flow (qL)
qL = weff
(Hu)i (10)
where L is the length of the channel, weff represents an effective width given by weff = AOF
Lkin . Here, AOF represents the area of the overland flow
region and Lkin is the total sum of the length of the kinematic elements and Lchan is the total length of the channel. (Hu)i is the discharge at the right end of kinematic element i . The index i goes through all the kinematic elements connected to the particular channel.
P. Neupane Research Overview February 5th, 2016 19 / 35
Recent Work 2-D Overland Flow
2-D Overland Flow Simulation
Run a simulation with the same conditions as parking lot 1, but now represent the parking lot as a 2-D domain and connect the parking lot to a channel below that receives the rainfall runoff. Check to see if the total amount of water collected is equal to the total amount of rainfall received.
x
0.0
0.5
1.0
y
0
200
400
600
0.0
0.5
1.0
Recent Work 2-D Overland Flow
2-D Overland Flow Results
time (m)
Corrected
Uncorrected
Analytic
Figure: Total discharge rate at the end of the parking lot for manually specified (corrected) flow path and the flow path calculated using the algorithm presented before (uncorrected).
0 10 20 30 40 50 60
time (m)
Corrected
Uncorrected
Analytic
Figure: Total water collected in the channel for manually specified (corrected) flow path and the flow path calculated using the algorithm presented before (uncorrected).
P. Neupane Research Overview February 5th, 2016 21 / 35
Recent Work 2-D Overland Flow
2-D Overland Flow Results
Solution is even worse with fully unstructured grids
An algorithm that computes a flow path that is not entirely physical results in an incorrect solution
Longer than physical flow paths subject flow to a “higher” resistance, causing decrease in flow rates
Need a more sophisticated technique to calculate flow paths!
However, when the flow path is accurate, the water volume collected in the channel is correct, implying that the coupling conditions work.
P. Neupane Research Overview February 5th, 2016 22 / 35
Recent Work Shallow Water Region
So Let’s Move On
Let’s simulate the whole process!
P. Neupane Research Overview February 5th, 2016 23 / 35
Recent Work Shallow Water Region
The Bay
Connect bay (shallow water region) to channels
Allows for draining rainfall runoff from land to channels to bay and for storm surge to propagate up the channels
Interface condition prescribed through numerical flux in a manner similar to coupling channel segments with junction regions
P. Neupane Research Overview February 5th, 2016 24 / 35
Recent Work Shallow Water Region
Numerical Flux
( (wh)in − (wh)ex
Recent Work Shallow Water Region
Numerical Flux
( (wh)in − (wh)ex
λ2D 1 = unx + vny −
√ gH
|Λ| = |λi | I R(:, i) = ri
where I is either a 2x2 or a 3x3 Identity matrix.
P. Neupane Research Overview February 5th, 2016 25 / 35
Recent Work Shallow Water Region
Numerical Flux
( (wh)in − (wh)ex
Recent Work Shallow Water Region
Interface conditions
Interface conditions imposed as exterior states at the nodes in the channel segments and at the edges of the triangulation of the shallow water region in the DG treatment
Interface conditions have to account for the difference in the dimensions of channel segments and shallow water regions.
Let E denote width of the shallow water edge connected to a channel and nchannel denote the outward unit normal vector of the channel at the interface node.
ζ2D i ,ex = ζ1D
Recent Work Shallow Water Region
Interface conditions
Interface conditions imposed as exterior states at the nodes in the channel segments and at the edges of the triangulation of the shallow water region in the DG treatment
Interface conditions have to account for the difference in the dimensions of channel segments and shallow water regions.
Let E denote width of the shallow water edge connected to a channel and nchannel denote the outward unit normal vector of the channel at the interface node.
ζ2D i ,ex = ζ1D
Recent Work Shallow Water Region
Coupled Execution
Provide coupling condition (qL) to connected channels
Evolve channels to the next time step
Provide interface conditions from channels to DGSWEM
Evolve DGSWEM to the next time step
Provide interface conditions from DGSWEM to channels
Apply necessary boundary conditions
Water Flowing into Bay through Channel
Entire domain is flat. The animation on the left shows the result of a simulation done with DGSWEM on the entire domain. The animation on the right shows the result of coupling DGSWEM with the channel.
P. Neupane Research Overview February 5th, 2016 28 / 35
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var ocgs=host.getOCGs(host.pageNum);for(var i=0;i<ocgs.length;i++){if(ocgs[i].name=='MediaPlayButton1'){ocgs[i].state=false;}}
Recent Work Tests for Coupling between Bay and Channel
Water Flowing into Channel through Bay
The bay is flat and the channel slopes upward. The animation on the left shows the result of a simulation done with DGSWEM on the entire domain. The animation on the right shows the result of coupling DGSWEM with the channel.
P. Neupane Research Overview February 5th, 2016 29 / 35
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Recent Work How about Flooding?
Flooding
Channels flood their banks when the water in them exceeds their capacity
Floodwater travels up the banks
Kinematic wave equations cannot handle this reverse flow direction
Convert the overland flow region to a 2D region in this case to simulate flooding
P. Neupane Research Overview February 5th, 2016 30 / 35
Recent Work How about Flooding?
Flooding the Channels
If Ve > Vcap,e :
qL = Vcap,e − Ve
Recent Work How about Flooding?
Flooding the Banks
On the floodplain edge connected to channels, prescribe a flow boundary condition:
Qboundary = qL
Recent Work How about Flooding?
So Let’s See If This Works
P. Neupane Research Overview February 5th, 2016 33 / 35
var ocgs=host.getOCGs(host.pageNum);for(var i=0;i<ocgs.length;i++){if(ocgs[i].name=='MediaPlayButton4'){ocgs[i].state=false;}}
Future Work
2 Recap Modeling Framework Channel Networks
3 Recent Work Kinematic Wave Equation 2-D Overland Flow Shallow Water Region Tests for Coupling between Bay and Channel How about Flooding?
4 Future Work
Future Work
Future Work
Simulate realistic watershed and the entire process
Perform analytical studies on the stability of the simulation process
P. Neupane Research Overview February 5th, 2016 34 / 35
Future Work
References I
surge_overview, October 2008. Accessed : 2015-10-26.
[3] Cevza Melek Kazezylmaz-Alhan, Miguel A Medina, and Prasada Rao. On numerical modeling of overland flow. Applied Mathematics and Computation, 166(3):724–740, 2005.
P. Neupane Research Overview February 5th, 2016 35 / 35
How about Flooding?
&
This material is based upon work supported by the National Science Foundation under Grant DMS - 1217071.
Motivation
Outline
2 Recap Modeling Framework Channel Networks
3 Recent Work Kinematic Wave Equation 2-D Overland Flow Shallow Water Region Tests for Coupling between Bay and Channel How about Flooding?
4 Future Work
Motivation
Motivation
Figure: Harris County Flood Control high water mark data for Harris and portions of Galveston County from hurricane Ike surge2.
P. Neupane Research Overview February 5th, 2016 2 / 35
Motivation
Motivation
There are multiple softwares that simulate hurricane storm surge like ADCIRC, SLOSH (Sea, Lake and Overland Surges from Hurricanes), P-Surge (Probabilistic Hurricane Storm Surge) etc.
There are multiple softwares that simulate rainfall runoff in watersheds like HEC-RAS, MIKE21, FLO-2D etc.
However, there is no software that simulates the effects of storm surge combined with rainfall.
Goal: Develop a simulation engine that couples rainfall with storm surge to simulate flooding in coastal watersheds
P. Neupane Research Overview February 5th, 2016 3 / 35
Recap
Outline
2 Recap Modeling Framework Channel Networks
3 Recent Work Kinematic Wave Equation 2-D Overland Flow Shallow Water Region Tests for Coupling between Bay and Channel How about Flooding?
4 Future Work
Recap Modeling Framework
Introduction
Watershed - A geographic extent that shares a common drainage point, often called a sink
Coastal watersheds - usually drain to a bay/ocean
Key components of coastal watershed hydrology - Overland flow/rainfall runoff, channel/river flow and coastal flow
Figure: An illustration of a coastal watershed that includes key components of watershed hydrology1
P. Neupane Research Overview February 5th, 2016 4 / 35
Recap Modeling Framework
1 Overland flow region → land that receives rainfall
2 Channels → networks of drainage channels and rivers that receive water from overland flow region and carry it to a drainage point X
May contain junctions of different channels X
3 Shallow water region → part of the coast and ocean to where all the water from the watershed drains X
Handled by DGSWEM - Discontinuous Galerkin Shallow Water Equations Model
P. Neupane Research Overview February 5th, 2016 5 / 35
Recap Modeling Framework
∂
Recap Channel Networks
(2)
s → curvilinear coordinate along the centerline of the channel A→ wet cross-section area (L2) Q = uA→ mean cross-sectional volumetric discharge (L3/T ) β → dimensionless momentum flux correction factor (between 1 and 1.06 for normal channels) qL → lateral inflow rate per until length of channel (L3/T/L)
P. Neupane Research Overview February 5th, 2016 7 / 35
Recap Channel Networks
(2)
S0 = ∂z ∂s → bed slope; z is the bathymetric depth (positive downwards)
Sf → friction slope estimated using the Manning friction relationship: Sf = n2Q|Q| A2H
4 3
I1 = ∫ d
0 (d − y)W dy → hydrostatic pressure term; W → width of the channel
I2 = ∫ d
P. Neupane Research Overview February 5th, 2016 7 / 35
Recap Channel Networks
Recap Channel Networks
Channels
Network of channels are decomposed into 1-D channels and 2-D junctions
2-D shallow water equations are solved in the junctions
Equations solved using a 2-stage Runge-Kutta discontinuous Galerkin method
Coupling of 1-D channels and 2-D junctions handled via the numerical flux
P. Neupane Research Overview February 5th, 2016 8 / 35
Recent Work
2 Recap Modeling Framework Channel Networks
3 Recent Work Kinematic Wave Equation 2-D Overland Flow Shallow Water Region Tests for Coupling between Bay and Channel How about Flooding?
4 Future Work
Recent Work
Recent Work Kinematic Wave Equation
Overland flow region
Think of overland flow as a uniform flow in a wide channel with rectangular cross-sections in the direction of the surface slope gradient
This implies a balance between the gravitational force S0 and the frictional force (Sf ) in the momentum equation of (2) resulting in:
u = n−1 √ S0H
Kinematic Wave Equation
∂x (F ) = qL (4)
where x is the coordinate in the direction of the surface slope, F = Hu and u is given by (3), and qL = R − I , where R is rainfall intensity and I is infiltration.
P. Neupane Research Overview February 5th, 2016 10 / 35
Recent Work Kinematic Wave Equation
Discontinuous Galerkin Finite Element Method
Given a domain = (a, b) let h = N−1 e=0
e = N−1 e=0
(xL, xR)e be the finite
element partition of into a set of non-overlapping elements e . Let Vh =
{ v ∈ L2() : v |e ∈ Pk (e) ∀ e ∈ h
} .
Multiply (4) by φ ∈ Vh, integrating over e , rearrange and approximate H by Hh ∈ Vh to get:∫ xR
xL
∂Hh
− Fφ|xR +
qLφ dx (5)
where F represents a numerical flux that is defined such that it is continuous across element boundaries. Take F to be the upwind flux, i.e. F = FL.
P. Neupane Research Overview February 5th, 2016 11 / 35
Recent Work Kinematic Wave Equation
Space-Time Representation
Let ψi be a set of basis functions for Pk (e).Then, over an element e :
Hh(x , t) = N∑
Hj (t)ψj (x) (6)
where Hj are the time-dependent coefficients of expansion of Hh in the ψj
basis. Differentiate the above equation in time and substitute it in the DG equation (5):∑
j
∂Hj
∂t
∫ xR
xL
+
Recent Work Kinematic Wave Equation
Space-Time Representation
Replace φ in (7) with each of the basis functions ψj to obtain the following system of ordinary differential equations:
Me d
+
Recent Work Kinematic Wave Equation
Runge–Kutta Discretization
Discretize the set of ODEs given in (8) using strong stability preserving (SSP) explicit 2-stage Runge–Kutta time stepping methods.
H1 = Ht + tL(Ht)
Ht+1 = 1
Recent Work Kinematic Wave Equation
Parking Lot 1
receives rainfall at an intensity of 2in./h
calculate the outflow rate at the end of the parking lot for 60 min
analytical solution given in Kazezylmaz-Alhan et al.3
0 10 20 30 40 50 60
time (m)
DG Solution
Analytic Solution
Figure: Plot of the numerical solution obtained using 400 elements to discretize the parking lot along with the analytical solution.
P. Neupane Research Overview February 5th, 2016 15 / 35
Recent Work Kinematic Wave Equation
Parking Lot 2
100 ft long with slope = 0.005
receives rainfall at an intensity of 2in./h for the first 3 min increased to 4 in./h for the second 3 min
calculate the outflow rate at the end of the parking lot for 20 min
semi-analytical solution obtained by superposition of the outflow rates for each individual period of the two-period storm3
0 5 10 15 20
time (m)
DG Solution
First Storm
Second Storm
Semi-analytic Solution
Figure: Numerical solution obtained using 150 elements to discretize the parking lot.
P. Neupane Research Overview February 5th, 2016 16 / 35
Recent Work 2-D Overland Flow
P. Neupane Research Overview February 5th, 2016 17 / 35
Recent Work 2-D Overland Flow
Algorithm to Route Kinematic Flow in a 2-D Region
Discretize overland flow region with triangular elements
The three edges of a triangle are the three possible flow directions
Pick the edge with the lowest elevation at the midpoint to be the flow edge
Each arrow in the diagram represents a kinematic element
On each kinematic element, solve the kinematic wave equation
Add the fluxes coming into an element if that element receives water from multiple elements
P. Neupane Research Overview February 5th, 2016 18 / 35
Recent Work 2-D Overland Flow
Connect Overland Flow Region with Channels
Channels receive flow from overland flow region as lateral flow (qL)
qL = weff
(Hu)i (10)
where L is the length of the channel, weff represents an effective width given by weff = AOF
Lkin . Here, AOF represents the area of the overland flow
region and Lkin is the total sum of the length of the kinematic elements and Lchan is the total length of the channel. (Hu)i is the discharge at the right end of kinematic element i . The index i goes through all the kinematic elements connected to the particular channel.
P. Neupane Research Overview February 5th, 2016 19 / 35
Recent Work 2-D Overland Flow
2-D Overland Flow Simulation
Run a simulation with the same conditions as parking lot 1, but now represent the parking lot as a 2-D domain and connect the parking lot to a channel below that receives the rainfall runoff. Check to see if the total amount of water collected is equal to the total amount of rainfall received.
x
0.0
0.5
1.0
y
0
200
400
600
0.0
0.5
1.0
Recent Work 2-D Overland Flow
2-D Overland Flow Results
time (m)
Corrected
Uncorrected
Analytic
Figure: Total discharge rate at the end of the parking lot for manually specified (corrected) flow path and the flow path calculated using the algorithm presented before (uncorrected).
0 10 20 30 40 50 60
time (m)
Corrected
Uncorrected
Analytic
Figure: Total water collected in the channel for manually specified (corrected) flow path and the flow path calculated using the algorithm presented before (uncorrected).
P. Neupane Research Overview February 5th, 2016 21 / 35
Recent Work 2-D Overland Flow
2-D Overland Flow Results
Solution is even worse with fully unstructured grids
An algorithm that computes a flow path that is not entirely physical results in an incorrect solution
Longer than physical flow paths subject flow to a “higher” resistance, causing decrease in flow rates
Need a more sophisticated technique to calculate flow paths!
However, when the flow path is accurate, the water volume collected in the channel is correct, implying that the coupling conditions work.
P. Neupane Research Overview February 5th, 2016 22 / 35
Recent Work Shallow Water Region
So Let’s Move On
Let’s simulate the whole process!
P. Neupane Research Overview February 5th, 2016 23 / 35
Recent Work Shallow Water Region
The Bay
Connect bay (shallow water region) to channels
Allows for draining rainfall runoff from land to channels to bay and for storm surge to propagate up the channels
Interface condition prescribed through numerical flux in a manner similar to coupling channel segments with junction regions
P. Neupane Research Overview February 5th, 2016 24 / 35
Recent Work Shallow Water Region
Numerical Flux
( (wh)in − (wh)ex
Recent Work Shallow Water Region
Numerical Flux
( (wh)in − (wh)ex
λ2D 1 = unx + vny −
√ gH
|Λ| = |λi | I R(:, i) = ri
where I is either a 2x2 or a 3x3 Identity matrix.
P. Neupane Research Overview February 5th, 2016 25 / 35
Recent Work Shallow Water Region
Numerical Flux
( (wh)in − (wh)ex
Recent Work Shallow Water Region
Interface conditions
Interface conditions imposed as exterior states at the nodes in the channel segments and at the edges of the triangulation of the shallow water region in the DG treatment
Interface conditions have to account for the difference in the dimensions of channel segments and shallow water regions.
Let E denote width of the shallow water edge connected to a channel and nchannel denote the outward unit normal vector of the channel at the interface node.
ζ2D i ,ex = ζ1D
Recent Work Shallow Water Region
Interface conditions
Interface conditions imposed as exterior states at the nodes in the channel segments and at the edges of the triangulation of the shallow water region in the DG treatment
Interface conditions have to account for the difference in the dimensions of channel segments and shallow water regions.
Let E denote width of the shallow water edge connected to a channel and nchannel denote the outward unit normal vector of the channel at the interface node.
ζ2D i ,ex = ζ1D
Recent Work Shallow Water Region
Coupled Execution
Provide coupling condition (qL) to connected channels
Evolve channels to the next time step
Provide interface conditions from channels to DGSWEM
Evolve DGSWEM to the next time step
Provide interface conditions from DGSWEM to channels
Apply necessary boundary conditions
Water Flowing into Bay through Channel
Entire domain is flat. The animation on the left shows the result of a simulation done with DGSWEM on the entire domain. The animation on the right shows the result of coupling DGSWEM with the channel.
P. Neupane Research Overview February 5th, 2016 28 / 35
var ocgs=host.getOCGs(host.pageNum);for(var i=0;i<ocgs.length;i++){if(ocgs[i].name=='MediaPlayButton0'){ocgs[i].state=false;}}
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Recent Work Tests for Coupling between Bay and Channel
Water Flowing into Channel through Bay
The bay is flat and the channel slopes upward. The animation on the left shows the result of a simulation done with DGSWEM on the entire domain. The animation on the right shows the result of coupling DGSWEM with the channel.
P. Neupane Research Overview February 5th, 2016 29 / 35
var ocgs=host.getOCGs(host.pageNum);for(var i=0;i<ocgs.length;i++){if(ocgs[i].name=='MediaPlayButton2'){ocgs[i].state=false;}}
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Recent Work How about Flooding?
Flooding
Channels flood their banks when the water in them exceeds their capacity
Floodwater travels up the banks
Kinematic wave equations cannot handle this reverse flow direction
Convert the overland flow region to a 2D region in this case to simulate flooding
P. Neupane Research Overview February 5th, 2016 30 / 35
Recent Work How about Flooding?
Flooding the Channels
If Ve > Vcap,e :
qL = Vcap,e − Ve
Recent Work How about Flooding?
Flooding the Banks
On the floodplain edge connected to channels, prescribe a flow boundary condition:
Qboundary = qL
Recent Work How about Flooding?
So Let’s See If This Works
P. Neupane Research Overview February 5th, 2016 33 / 35
var ocgs=host.getOCGs(host.pageNum);for(var i=0;i<ocgs.length;i++){if(ocgs[i].name=='MediaPlayButton4'){ocgs[i].state=false;}}
Future Work
2 Recap Modeling Framework Channel Networks
3 Recent Work Kinematic Wave Equation 2-D Overland Flow Shallow Water Region Tests for Coupling between Bay and Channel How about Flooding?
4 Future Work
Future Work
Future Work
Simulate realistic watershed and the entire process
Perform analytical studies on the stability of the simulation process
P. Neupane Research Overview February 5th, 2016 34 / 35
Future Work
References I
surge_overview, October 2008. Accessed : 2015-10-26.
[3] Cevza Melek Kazezylmaz-Alhan, Miguel A Medina, and Prasada Rao. On numerical modeling of overland flow. Applied Mathematics and Computation, 166(3):724–740, 2005.
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How about Flooding?