The document discusses validating numerical models of storm surges using analytical solutions. It presents results from benchmark tests comparing the D-Flow FM model's solutions for water level and velocity against exact analytical solutions under controlled conditions. Good agreement was found between the model and analytical solutions when assumptions and parameters were closely matched, demonstrating the model solves the governing equations correctly.

1. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Storm Surges Validation
The State-of-the-Play for D-Flow FM
watermotion.eu | waterbeweging.nl
Giordano Lipari
5.11.2014
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

2. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Watermotion.eu | Expertise, Services, Products
Consultancy
Dissemination
Marketing
Research

3. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Watermotion.eu | Expertise, Services, Products
Consultancy
Dissemination
Marketing
Research
Simulations Data Analysis
Capacity Building Reviewing

4. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Watermotion.eu | Expertise, Services, Products
Consultancy
Dissemination
Marketing
Research
Simulations Data Analysis
Capacity Building Reviewing
Information Data
Knowledge

5. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Watermotion.eu | Expertise, Services, Products
Consultancy
Dissemination
Marketing
Research
Simulations Data Analysis
Capacity Building Reviewing
Information Data
Knowledge
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

6. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
As many approaches as facets
Never forget reality
Equations from Physics, Solutions from Mathematics
Hydrodynamics on All Fours
Hydrodynamics calculation
analytical
numerical
context
knowledge
measurements
physics
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

7. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
As many approaches as facets
Never forget reality
Equations from Physics, Solutions from Mathematics
Words of Caution
Tri
e-worship, belief in answers, connectionism, black box mistake, methodolatry, dead-

8. sh
fallacy, Jehovah problem
bit.ly/7defects (publisher)
bit.ly/

9. nd7defects (Google search)
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

10. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
As many approaches as facets
Never forget reality
Equations from Physics, Solutions from Mathematics
Man is the measure of all things"
Crosby Beach, UK. 'Another Place' by Antony Gormley
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

11. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
As many approaches as facets
Never forget reality
Equations from Physics, Solutions from Mathematics
Man is the measure of all things"
Crosby Beach, UK. 'Another Place' by Antony Gormley
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

12. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
As many approaches as facets
Never forget reality
Equations from Physics, Solutions from Mathematics
Man is the measure of all things"
Crosby Beach, UK. 'Another Place' by Antony Gormley
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

13. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
As many approaches as facets
Never forget reality
Equations from Physics, Solutions from Mathematics
Man is the measure of all things"
Crosby Beach, UK. 'Another Place' by Antony Gormley
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

14. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
As many approaches as facets
Never forget reality
Equations from Physics, Solutions from Mathematics
Physics and Computations
Equations from physics
I Trustworthy cause-eect relations
I Raison d'^etre of equations
I Delft3D, D-Flow FM
Shallow-water (depth-averaged,
long-wave) equations
I Water: Forces ! Motion ! Forces
! ...
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

15. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
As many approaches as facets
Never forget reality
Equations from Physics, Solutions from Mathematics
Physics and Computations
Equations from physics
I Trustworthy cause-eect relations
I Raison d'^etre of equations
I Delft3D, D-Flow FM
Shallow-water (depth-averaged,
long-wave) equations
I Water: Forces ! Motion ! Forces
! ...
I Validation of a choice
I Solving the right equations...
I and/or choosing the right
interpretation?
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

16. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
As many approaches as facets
Never forget reality
Equations from Physics, Solutions from Mathematics
Physics and Computations
Equations from physics
I Trustworthy cause-eect relations
I Raison d'^etre of equations
I Delft3D, D-Flow FM
Shallow-water (depth-averaged,
long-wave) equations
I Water: Forces ! Motion ! Forces
! ...
I Validation of a choice
I Solving the right equations...
I and/or choosing the right
interpretation?
Solutions from computation
Analytical solutions
I exact (absolute credibility)
I restrictive assumptions
I limited applicability
I results easy to interpret
Numerical solutions
I approximate (conditional credibility)
I
exible scope, wide applicability
I results harder to interpret
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

17. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
As many approaches as facets
Never forget reality
Equations from Physics, Solutions from Mathematics
Physics and Computations
Equations from physics
I Trustworthy cause-eect relations
I Raison d'^etre of equations
I Delft3D, D-Flow FM
Shallow-water (depth-averaged,
long-wave) equations
I Water: Forces ! Motion ! Forces
! ...
I Validation of a choice
I Solving the right equations...
I and/or choosing the right
interpretation?
Solutions from computation
Analytical solutions
I exact (absolute credibility)
I restrictive assumptions
I limited applicability
I results easy to interpret
Numerical solutions
I approximate (conditional credibility)
I
exible scope, wide applicability
I results harder to interpret
Veri

18. cation of a procedure
I Are we solving the equations right?
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

19. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Building a model
The message of the benchmarks
Space | Size | Contour | Forces | Response?
How to build an exact and useful model

20. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Building a model
The message of the benchmarks
Space | Size | Contour | Forces | Response?
How to build an exact and useful model
L
B
D

21. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Building a model
The message of the benchmarks
Space | Size | Contour | Forces | Response?
How to build an exact and useful model
L
B
D

22. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Building a model
The message of the benchmarks
Space | Size | Contour | Forces | Response?
How to build an exact and useful model
L
B
D

23. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Building a model
The message of the benchmarks
Space | Size | Contour | Forces | Response?
How to build an exact and useful model
L
B
D
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

24. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Building a model
The message of the benchmarks
Harbour of IJmuiden
A look-alike
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

25. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Building a model
The message of the benchmarks
Numerical models can be objectively tested
Books and journals
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

26. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Building a model
The message of the benchmarks
Exact water-level and currents driven by the wind
On a longitudinal transect (marked orange)
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

27. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Building a model
The message of the benchmarks
Exact water-level and currents driven by the wind
Side view on the longitudinal cross section. Blue = water level. Green = velocity
2
1
0
−1
−2
E=F0*L/(gH)
U=F0*L/H(gH)^½
0.109
0.0
Profiles | t/T=1/360 [min] ; H= 10 m W= 25.0 m/s
0.0 0.2 0.4 0.6 0.8 1.0
x/L {L=5000 m}
e/E, u/U {E=0.064 m, U=0.063 m/s
0.109
0.0
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

28. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Solving the right equations right
Testing correctness in D-Flow FM
Hydrodynamics calculation
analytical
numerical
context
knowledge
measurements
physics
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

29. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Computational grid
Delta Shell: observation points and cross sections
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

30. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Water-level history. Map view
W=25 m/s; h0 = 10m/s; = 103 m/s; t = 5 s. Non linear terms turned o
The darker the shade, the deeper the water
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

31. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Water-level history. Downwind location (inundation)
W=25 m/s; h0 = 10m/s; = 103 m/s; t = 5 s. Non linear terms turned o.
Blue line: D-Flow FM. Red line: exact solution
2.0
1.5
1.0
0.5
0.0 0.2 0.4 0.6 0.8 1.0
t/T {T=21600.0 s}
0.0
e/E {E=F0*L/(gH)=0.064 m}
History water level at x/L=5000.0/5000 [ST3d]
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

32. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Water-level history. Mid-basin location
W=25 m/s; h0 = 10m/s; = 103 m/s; t = 5 s. Non-linear terms turned o.
Blue line: D-Flow FM. Red line: exact solution
1.0
0.8
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
t/T {T=21600.0 s}
−0.2
e/E {E=F0*L/(gH)=0.064 m}
History water level at x/L=2500.0/5000 [ST3d]
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

33. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Water-level history. First-quarter upwind location
W=25 m/s; h0 = 10m/s; = 103 m/s; t = 5 s. Non-linear terms turned o.
Blue line: D-Flow FM. Red line: exact solution
0.5
0.4
0.3
0.2
0.1
0.0
0.0 0.2 0.4 0.6 0.8 1.0
t/T {T=21600.0 s}
−0.1
e/E {E=F0*L/(gH)=0.064 m}
History water level at x/L=1250.0/5000 [ST3d]
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

34. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Velocity history. Map view
W=25 m/s; h0 = 10m/s; = 103 m/s; t = 5 s. Non linear terms turned o
Red shades: net
ow in. Blue shades: net
ow out. White: zero net
ow
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

35. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Velocity history. Upwind location (open boundary)
W=25 m/s; h0 = 10m/s; = 103 m/s; t = 5 s. Non-linear terms turned o.
Green line: D-Flow FM. Red line: exact solution
1.0
0.5
0.0
−0.5
0.0 0.2 0.4 0.6 0.8 1.0
t/T {T=21600.0 s}
−1.0
q/Q {Q=F0*L/(gH)^½=0.631 m²/s}
History depth-averaged velocity at x/L=0.0/5000 [ST3d]
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

36. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Velocity history. Mid-basin location
W=25 m/s; h0 = 10m/s; = 103 m/s; t = 5 s. Non-linear terms turned o.
Green line: D-Flow FM. Green line: exact solution
0.6
0.4
0.2
0.0
−0.2
−0.4
0.0 0.2 0.4 0.6 0.8 1.0
t/T {T=21600.0 s}
−0.6
q/Q {Q=F0*L/(gH)^½=0.631 m²/s}
History depth-averaged velocity at x/L=2500.0/5000 [ST3d]
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

37. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Velocity history. Third-quarter downwind location
W=25 m/s; h0 = 10m/s; = 103 m/s; t = 5 s. Non-linear terms turned o.
Blue line: D-Flow FM. Red line: exact solution
0.3
0.2
0.1
0.0
−0.1
−0.2
0.0 0.2 0.4 0.6 0.8 1.0
t/T {T=21600.0 s}
−0.3
q/Q {Q=F0*L/(gH)^½=0.631 m²/s}
History depth-averaged velocity at x/L=3750.0/5000 [ST3d]
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

38. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Introducing a bit of challenge
A meander-like grid (but there's no meander). Skewed grid and
ow.
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

39. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Water-level history. Mid-basin location
Skewed
ow and grid ... Non-linear terms turned-o.
Blue line: D-Flow FM. Red line: exact solution
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
t/T {T=21600.0 s}
−0.2
e/E {E=F0*L/(gH)=0.064 m}
History water level at x/L=2500.0/5000 [ST3h]
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

40. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Velocity history. Mid-basin location
Skewed
ow and grid ... Non-linear terms turned-o.
Green line: D-Flow FM. Red line: exact solution
0.6
0.4
0.2
0.0
−0.2
−0.4
0.0 0.2 0.4 0.6 0.8 1.0
t/T {T=21600.0 s}
−0.6
q/Q {Q=F0*L/(gH)^½=0.631 m²/s}
History depth-averaged velocity at x/L=2500.0/5000 [ST3h]
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

41. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Time-step sensitivity
Increasing the time step from a sound 5 s to 30 s
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

42. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Water-level history. Mid-basin location
Time-step sensitivity. W=25 m/s; h0 = 10m/s; = 103 m/s; t = 30 s.
Blue line: D-Flow FM. Red line: exact solution
1.0
0.8
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
t/T {T=21600.0 s}
−0.2
e/E {E=F0*L/(gH)=0.064 m}
History water level at x/L=2500.0/5000 [ST3g]
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

43. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Solving the right equations right
Comparison with close match of assumptions and settings
The grid challenge
Time-stepping
Velocity history. Mid-basin location
Time-step sensitivity. W=25 m/s; h0 = 10m/s; = 103 m/s; t = 30 s.
Green line: D-Flow FM. Red line: exact solution
0.6
0.4
0.2
0.0
−0.2
−0.4
0.0 0.2 0.4 0.6 0.8 1.0
t/T {T=21600.0 s}
−0.6
q/Q {Q=F0*L/(gH)^½=0.631 m²/s}
History depth-averaged velocity at x/L=2500.0/5000 [ST3g]
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

44. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
State of the Play: Hop Jump Spring
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

45. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
State of the Play: Hop Jump Spring
I Solving the right equations Solving the equations right
I Analytical solutions Exact credibility at the cost of limited scope
I Numerical methods All options can be guaged against a reference
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

46. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
State of the Play: Hop Jump Spring
I Solving the right equations Solving the equations right
I Analytical solutions Exact credibility at the cost of limited scope
I Numerical methods All options can be guaged against a reference
I Storm surges Unsteady long waves. The more accurate the better
I D-Flow FM simulates the velocity and water level oscillations well
I Source code can be made compliant to benchmarks (transparency)
I Follow good modelling practices to avoid inaccuracy (expectedly)
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

47. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
State of the Play: Hop Jump Spring
I Solving the right equations Solving the equations right
I Analytical solutions Exact credibility at the cost of limited scope
I Numerical methods All options can be guaged against a reference
I Storm surges Unsteady long waves. The more accurate the better
I D-Flow FM simulates the velocity and water level oscillations well
I Source code can be made compliant to benchmarks (transparency)
I Follow good modelling practices to avoid inaccuracy (expectedly)
I Now Leveraging more information from the current test case
I Soon Comparison with Delft3D
I Then Test cases for similar wind-driven
ows
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

48. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Thanks and Credits
Deltares sta (they did dare to share!):
Arthur van Dam, Edward Melger, Herman Kernkamp, Sander van
der Pijl
Flickr contributors: Beverley Goodwin, Chris Saxman, Terry Kerney
PNG/Tikz community for graphics templates
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play

49. Watermotion.eu
Hydrodyamics before Equations
The Help from Analytical Solutions
Solving the right equations right
Summing up
Thanks for your attention
Hope this has been been useful
www.watermotion.eu
www.waterbeweging.nl
watermotion.eu | waterbeweging.nl Storm Surges Validation for D-Flow FM: the State of the Play