Presentation by Mart Borsboom (Deltares) at the XBeach X (10th Year Anniversary) Conference, during Delft Software Days - Edition 2017. Friday, 3 November 2017, Delft.

1. 3 November 2017
Xbeach X Conference, 1-3 November 2017, Delft
An analysis of the morphodynamic
acceleration technique (MorFac)
Mart Borsboom, Dirk-Jan Walstra, Liang Li (TUD),
Roshanka Ranasinghe (IHE)

2. 3 November 2017
Contents
• MorFac ( ) in the computational model
• 1D model problem
• Some results
• Analysis and prediction
• Some more results
• Concluding remarks
Ranasinghe, Swinkels, Luijendijk, Roelvink, Bosboom, Stive, Walstra (2011), Morphodynamic
upscaling with the MORFAC approach: dependencies and sensitivities, Coast. Eng. 58, 806—811
MF

3. 3 November 2017
A morphodynamic model
continuous
model
discretized
model
Delft3D-MOR
-dep.
discr.errors
MF
MF

4. 3 November 2017
1D channel flow
described by the continuous model:
• 1DH shallow-water equations
• 1D Exner equation
The model problem

5. 3 November 2017
Results
30 ,100 , 300 ,1000 , 3000MF 
 0 0 ,4m , 1.25m s , 0.2 , 0.001m , 20mb inith u Fr z x      
continuous model
discretized model (central/upwind Exner)
Delft3D-MOR (central/upwind Exner)
1200hoursT  3200hoursT 
(if present!)

6. 3 November 2017
Analysis of continuous problem
Model equations:
Perturbation analysis:
Fourier-mode analysis:
 
2
5
3 2
50
( )
0
0.05
1 ,
b
b B EH
EH B
z u
t x
g u uu u u
u g
t x x C h x x
z S u
MF S
t x gC D
 


 
 
  
 
 
     
      
     
 
  
  
with and Bagnold corr.
 ( , ) Z exp ( )b j j j
j
z x t ik x t  
,0 0 0, ,b b bz z z u u u          

7. 3 November 2017
2
0 0
0 2
0 0
1 1
min ,
2 2
Fr Fr
MF
Fr Fr
 
  
   
 
Analysis of continuous problem
Result of Fourier-mode analysis:
from which we obtain:
 
 
    
2
0 0 0
2
0 0 0
22
0 0 0 0
0
0
0
0
3
0 0
2
1
1 1
2
1
1 1
2
1 (1
2
)B
Fr MF O Fr
Fr MF O Fr
Fr MF Fr M
ik
Re ik
ik
Re ik
ikd M rF F FO
 
 


 




 
    
 
 
     
 


  

 
2
0 0 0 0
2
0 0
2 2
,
1 1
W B
Fr MF Fr MF
err err
Fr Fr
 
 
 

8. 3 November 2017
Analysis of continuous problem
Eigenvalues as function of forMF
  1 2 2
0 0 0
5
6 40
50 0 3 2
0 0 50
4m, 1.25m s, 0.2 ,C 65m s, 1.0m s, 0.396,
1 5 0.05
1, 1.65,D 350 10 m, 3.08 10
1
h u Fr
u
h u gC D
 

 

 
      
 
         
  
2 400mk 

9. 3 November 2017
 0 0 0 ,4m , 1.25m s , 0.2 , 0.001m , 20mb inith u Fr z x      
Results
30 ,100 , 300 ,1000 , 3000MF 
continuous model
discretized model (central/upwind Exner)
Delft3D-MOR (central/upwind Exner)
(if present!)
1200hoursT 

10. 3 November 2017
Small adaptation of Exner discretization
30 ,100 , 300 ,1000 , 3000MF 
continuous model
discretized model (central/upwind Exner,
(no Delft3D-MOR results yet)
( )EHS u implicit)
(if present!)
1200hoursT 
 0 0 0 ,4m , 1.25m s , 0.2 , 0.001m , 20mb inith u Fr z x      

11. 3 November 2017
Different initial perturbation
30 ,100 , 300 ,1000 , 3000MF 
continuous model
discretized model (central/upwind Exner)
(no Delft3D-MOR results yet)
(if present!)
1200hoursT 
 0 0 0 ,4m , 1.25m s , 0.2 , 0.001m , 20mb inith u Fr z x      

12. 3 November 2017
Concluding remarks
Analysis to:
• understand effect of MorFac, derive upper bounds for
• understand effect of discretization errors (can be very large!)
• improve numerical implementation
Linearized approach applicable to any perturbation of a smooth
solution.
When in doubt, analyze!
MF