1) The document discusses opportunities for next generation river modelling using flexible mesh approaches like DFM. It highlights the ability to refine meshes in areas like narrow channels and winter beds. 2) Subgrid scale techniques are presented for better representing phenomena like flooding/drying, non-linear volumes, flow over weirs and structures, and spiral flows. Comparisons with other models show improved accuracy with finer grids. 3) Performance tests on different case studies demonstrate the ability to refine grids locally while maintaining reasonable computation times compared to fixed grids. Further optimizations may integrate 1D representations and evaluate spiral flows with 2D or 3D approaches.

1. Opportunities for next generation river modelling
Herman Kernkamp
Delft Software Days, 05-10-2015

2. Transport, recreation

3. Beautiful Dangerous Dirty

4. Protect land, Manage the flow

5. Transport heat

6. Not only 2D

7. Scale, Predicatabilty, Meteo, Groundwater

8. Sobek1D-2D
8

9. Waqua
Triwaq
Delft-3D
9

10. DFM : Curvilinear + occasional triangle
10

11. Very small cells in winterbed
Aligned summerbed

12. Opportunities of the Flexible Mesh

13. Geometry : define flow area Au
  0u
u u u
u upwind u
A uV
t x
A W h
h b

 
 

 
uW
How define bedlevel at u-point ?
ub
(Trick of Guus saves the day)

14. Bedlevel defined by cell center or by cell cornerub
max( , )u L Rb b b
ubupw
Xbeach, Sobek1D2D Delft3D, DFM
Tile Netnode

15. Tested in channels with dx = 23 km to 180 m

16. Spatial convergence cell centre bathy.

17. Spatial convergence netnode bathy.

18. Dambreak test grids
18

19. Works fine on various grids IF no shear in flow
19
3D sigma

20. Poiseulle testcase: strong shear
20

21. Strong shear, aligned grid, local refinement
21

22. Strong shear, non-aligned triangles, no adv.
22

23. Advection works bad on non-aligned grids
23

24. Cure : Higher order cell velocity reconstruction
Mart, Frank implicit reconstruction yet to implemented in DFM
Mohamed, explicit reconstruction already showed promising results,
both for improving horizontal eddy viscosity terms and advection
terms, but.. sometimes it fails

25. Staircase : Conveyance = 80 percent of curvi

26. Cutcell : Conveyance = 100 percent of curvi

27. Cutcell: Approaching wall 1/3
Approaching wall not felt in cell 1 and 2
Sudden direction change in cell 3
Introduces advection losses
Approaching wall bij reduced flow area
Aligned cell center advection velocities
Smooth flow parallel to wall
1 2 3

28. Momentum conservation: Carnot losses
1 2 3
 
 
 
2 2
1 3 1 1 3 3 3 3
1 1 3 3
3 1 3 1 3
2 2 2
1 3
1 3
1 3
2
1 3
U U
U U
U U U
1
(U U )
2
U U
U U
2
1
(U )
2
Mom
Bern
Bern
Bern Mom
p A A p A A
A A
p p p
p
p
p p p U
 




  

    
  

  
       
Momentum 2-3 :
Bernoulli 2-3 :
Carnot loss 2-3 :
Reversed flow ; loss from 2 to 3 is equal to gain from 3 to 2

29. Flow from right to left, sudden expansions

30. Flow from right to left, sudden expansions

31. Flow from left to right, sudden contractions
Unphysical result, error in pressure assumption at position 2
better apply energy conservation in sudden contraction

32. Bed form in rivers
200 m

33. Smooth bed forms and numerical diffusion
No friction, smooth bed form => no setup
25 m
0.3 m
4 m

34. 10 november 2015
Untrim
Effect of the grid resolution for advection scheme A
(semi-Lagrangian):

35. 10 november 2015
Telemac
Effect of the grid resolution for advection scheme B
(semi-Lagrangian):

36. 10 november 2015
DFM
Effect of the grid resolution for advection scheme D
(“momentum-conservative, 2nd order accurate”):

37. Mesoscale horizontal flow-field modelling at a channel-river-junction
Hydraulic Engineering · W2 · R. Patzwahl, F. Platzek, J.A. Jankowski · 6th november 2013Page

38. Mesoscale horizontal flow-field modelling at a channel-river-junction
Hydraulic Engineering · W2 · R. Patzwahl, F. Platzek, J.A. Jankowski · 6th november 2013
SCALE MODEL
4 km of river stretch = 67 m of model length
Length Scaling: 1:60
Height Scaling: 1:30
Stationary discharge conditions, non-movable gravel bed
Page

39. Labor
D-Flow FM
Natur

40. Kam Tin Drainage channel
peak flows ~ 6 m/s
40
Subgrid : sloping bed

41. Continuous wet area => more gradual drying&flooding
41
classic
DFM

42. Subgrid: Analytic Conveyance approach
2
( )
( )
h(y)
C (y
R
)
U C Ri
Q AC R i K i
g
C
f
R
y
g
Uu
yU
u
j

 




iy
1iy 
42

43. Spatial convergence of subgrid approach
,470
,475
,480
,485
,490
,495
,500
,505
,510
,515
0 10 20 30 40 50 60
standard
2D conv
Flooding
Discharge
Capacity
m3/s
Nr of cells in cross-sectional direction.
3, 6, 12, 24 or 48 cells
43

44. So far:
Tile depth approach in D3D morphology (Bedlevtype = 6)
Flat bed at u-point,
Level : max level of adjacent cells
Netnode depth approach in D3D Wave coupling (Bedlevtype = 3)
Sloping bed at u point
Level : max level of adjacent cells
Hydraulic radius R = A/P (Conveyance2D = 1)
No implementation of sloping bed at u-point in 3D yet
So: if 2D and 3D should match, use
(Bedlevtype = 3)
(Conveyance2D = -1)
in both models.
Warning: default advection is still not o.k. icw sloping bed on velocity point and
no bed friction.

45. Singapore rainfall runoff: Non-linear volumes
45

46. Subgrid 2: non-linear volumes
 
 
 
1 1
1 1
1
0
p
p p p p
p p p p p
p p p p n
u u
out in
V
V V
V V A
V A V
A u A u
t


 

 
 
 
 


  

  
  
  

 
Thin water layer : Non – linear volume
Thick water layer : linear volume
46

47. Singapore rainfall runoff: Linear volumes
47

48. Singapore rainfall runoff: Non-linear volumes
48

49. Subgrid 3 : Flow over weir

50. Free weir discharge Qf : Everyone agrees
50
1 2
2 2 2
1 2
1 1 2 2 2
22 2 2
u u q
E
g g g
  

     
2
0
q




1 1
2 1
2
3 3
fq E g E
Everyone agrees: Maximum free weir discharge =2 1
2
3
E at
Waterlevels relative to crestlevel

51. Submerged weir discharge Qs : No one agrees
51
1) Villemonte (1947)
2 1
3 3 3
2
1s fq q S
 
  
 
2) Rajaratnam&Muralidhar (1969), (Bernoulli, 2 3h h ) 3 1 32 ( )sq h g E h  , or
3 3
(1 )
2
s fq q S S 
3) Varshni&Mohanty (1973), (0.03<S<1) 2
1.03 0.027 0.059s fq q S S   
4) Lakshmana Rao (1975) s fq q 
5) Abou-Seida and Quraishi (1976), (short crest)
1
1 1
2
s fq q S S
 
   
 
6) Wu and Rajaratnam (1996), (S<0.95)  1
1 1.162 1.33sin ( )s fq q S S
  
7) Tabellenboek fit (p = 20) (1 )p
s fq q S 
8) Borghei (2003)
B B
0.701-0.121 2.229 1.663
L L
s fq q S
    
      
    

52. Submerged discharge curve Qs/Qf vs S
52

53. Tabellenboek data

54. Analytic semi subgrid weir model:
54
Contraction Expansion
Energy conservation Momentum conservation
 
2 2
1
1
2 2
1
2 2
1
2
u
u u
g g
adv u u
x
   
 

1 1,u ,u u
1 1 2
2
max( ,min( , ) b)
3
uh E   
2 2,u
b

55. Qfree/Qsub – Submergence aligned grid

56. 45 degree

57. Flow width at weir u point
57
 u ulink weirW W n n
Sum of all weir links is equal to weir length

58. Qfree/Qsub – Submergence 45 deg grid

59. Width of default scheme
Velocity points involved in limited higher order
 
 
( ) ( )
1
1 ( ) ( )
1
out
inL outL
u
in out
inR outR
u L R
in u Q u u
V
Q u u Q u u
V V V
Q u

 
  
     
   
 
         
  
 
 
59

60. Many groyns and weirs in polygons x,y,z

61. Not always aligned in grid

62. Nijmegen quay

63. Some lines can do without weirscheme
Fixed weir treshold, e.g 0.5 m

64. Staircases

65. Aligned (high flow velocities next to quay)

66. Nijmegen quay bathymetry
DFM WAQUA

67. Take care interpolating bathymetry

68. Again geometry: Ks D3D style or Waqua style
12
18log
s
R
C
k
 
  
 
0
ln
g h
C
ez
 
  
 
‘gemiddeld tussen cirkel en breed kanaal’
Formule 13.15 in Vloeistofmechanica
WAQUA Style => Dykes can be lower

69. Spiral flow:
0
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
0,09
0,1
1 2 3 4 5 6 7 8 9 10 11 12
Spiral Intensity 1/s
Spiral…
Willem and Mohamed: Spiral Flow on unstructured net
Well under way: Influence on Morphology
Or: use 3D,
2, 3, 4, 5, 7,10,15,20 30 layers
0
5
10
15
20
25
0 5 10 15
cpu/cpu2D
cpu/cpu2D
Kmx = 2, cpu = 3*cpu2D
Kmx=30, cpu = 20*cpu2D
( Check weirs in 3D )

70. Herwijnen Pannerden

71. DFM A : 8 in summerbed , total 23000

72. DFM B : 16 in summerbed, total 59000

73. DFM C : 32 in summerbed, total 190000

74. Waqua : 13-14 in summerbed, total 122000

75. Grid convergence
Rooster Observatie DFM A DFM B DFM C DFM op
WAQUA rooster
Pannerdensekop 14.48 14.56 14.42 14.41 14.45
Nijmegen 12.30 12.47 12.33 12.33 12.34
Tiel 9.33 9.14 9.07 9.07 8.98
Zaltbommel 6.43 6.32 6.25 6.24 6.22
waterlevels

76. Computation times
DFM A DFM B DFM C DFM op
WAQUA
rooster
Aantal actieve
punten ()
22881 59331 187955 122328
Aantal
tijdstappen ()
8674 15161 35010 23826
Rekentijd (s) 228 959 8560 4243
Gemiddelde
tijdstap (s)
29.9 17.1 7.4 10.9
Tabel 3: Rekentijden voor 72 uur simulatie op Elitebook 8570w

77. Semi subgrid – tabellenboek, DFM A
Pannerdensekop +4 cm
Nijmegen +1 cm
Tiel +2 cm
Zaltbommel +2 cm

78. Discussion:
DFM makes it easier to refine some area and assess local modifications
DFM is still a lot slower than WAQUA , so how fine can the network be?
Can part of the network be 1D?
Does winterbed need same resolution as summerbed?
Spiral flow icw 2D or 3D instead? (Check subgrid weirs in 3D)
Trachytopen/Baptist/3D vegetation in winterbed ?
Bedform / roughness estimators in summerbed?
Hles? Settings for Regina’s problem? Higher order adv. in 3D problem!
Coupling to groundwater?
Non-linear volumes for dynamic high water simulation?

79. Is this true?
Summerbed friction is a certainty because of extensive land use
classification
== >
Winterbed is the only location where calibration is allowed.

80. Groundwater in DFM