nearshore wave-ﬂow modelling with swashnovember 1, 2011 4/37 environmental fluid mechanics section...

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Environmental Fluid Mechanics SectionDelft University of Technology

Nearshore wave-flow modellingwith SWASH

12th Waves Workshop

Marcel, Guus and Pieter

November 1, 2011

November 1, 2011 2/37

Environmental Fluid Mechanics Section

Motivation• Goal: to develop a model that is capable of simulating wave

motion (with current) in coastal waters up to the shore.

• Different levels of wave modelling:

• phase-averaging: statistical properties, spectral, SWAN.

• phase/wave-resolved: linear (MSE) and nonlinear

(NLSW, Boussinesq, Serre, Green-Naghdi).

• Non-hydrostatic wave-flow models (Navier-Stokes):

• permit wave breaking, runup, undertow, etc. derived

from first principles and well-founded semi-empirical

modelling, and

• appear to be very robust and are not prone to unstable.

November 1, 2011 3/37


Methodology• The simplest modelling for wave transformation is the nonlinear

shallow water (NLSW) equations.

• NLSW-type models exhibit conservation properties and are ableto deal with breaking/bore capturing, dike breach flooding, andtsunami inundation, among others.

• With the inclusion of non-hydrostatic pressure, many other wavephenomena (dispersion, surf beat, triads, etc.) can be describedin a natural manner as well.

• Water depth can be divided into a number of layers and therebytake into account vertical variation (e.g. undertow).

• Also, they improve their frequency dispersion by increasing thenumber of layers.

November 1, 2011 4/37


Summary of conclusions

• SWASH is a first push toward a quasi-operational, open

source non-hydrostatic model suitable for simulation of

coastal waves and runup.

• In case of nearshore wave modelling, SWASH appears to

be accurate, fast, robust and well tested.

• The computational algorithm combines efficiency and

robustness allowing application to large-scale, real-life

problems.

• Very few tunable parameters needed.

November 1, 2011 5/37


Introduction to SWASH

• Many variants (numerics) of non-hydrostatic models have

been proposed in the literature, exposing excellent features

such as frequency dispersion and nonlinear effects.

• However, no advances have been made in assessing those

models at an engineering level with observations under

realistic nearshore conditions.

• Over the past 10 years, strong efforts have been made at

Delft University to advance the state of wave modelling and

flooding simulations for coastal engineering.

• SWASH: it is essentially applicable in coastal regions up to

the shore: Simulating WAves till SHore.

November 1, 2011 6/37


SWASH − physics

SWASH accounts for the following physical phenomena:

• propagation, frequency dispersion, shoaling, refraction and

diffraction,

• flooding, wave runup, moving shoreline,

• nonlinear wave-wave interactions (surf beat, triads),

• wave-induced currents and wave-current interaction,

• wave breaking,

• bottom friction, and

• subgrid turbulence and vertical mixing.

November 1, 2011 7/37


SWASH − numerics

• Fully explicit; Courant-based time step restriction (but not

severe!).

• Vertical terms are semi-implicitly integrated using a

θ−scheme (12≤ θ ≤ 1).

• Staggered grid in space and time; second order in time and

no amplitude error.

• Finite differences in horizontal and finite volumes in vertical.

• Advection approximation by means of first or second order

upwind schemes with(out) flux limiting (BDF, Fromm,

MUSCL, QUICK, minmod, etc.).

November 1, 2011 8/37


− continued −

• Advection terms are approximated such that momentum

conservation is ensured. Important for wave breaking!

• Surface elevation through depth-averaged continuity

equation ensuring global mass conservation.

• A simple approach is adopted that tracks the moving

shoreline by ensuring

• non-negative water depths and

• using first or second order upwind water depths in the

momentum flux approximations. Flux limiters (MUSCL,

minmod, Van Leer, etc.) may be employed.

November 1, 2011 9/37


− continued −

• For accuracy reason, the pressure is split-up into hydrostatic

and non-hydrostatic parts.

• Second order projection method where correction to the

velocity field for the change in non-hydrostatic pressure is

incorporated (local mass conservation).

• Either SIP (depth-averaged mode) or (M)ILU-BiCGSTAB

(multi-layered mode) iterative solver is employed for the

solution of the pressure Poisson equation.

November 1, 2011 10/37


General layer concept

November 1, 2011 11/37


SWASH − functionalities

• Wave makers:

• Fourier series, time series, or

• 1D, 2D spectrum; parametric (PM, Jonswap or TMA),

SWAN or observations.

• Weakly reflective, Sommerfeld, sponge layers.

• Rectilinear or orthogonal curvilinear.

• Cartesian or spherical coordinates.

• 1D-mode (flume) or 2D-mode (basin).

• Depth-averaged or multi-layered mode.

November 1, 2011 12/37


− continued −

• Physics: bottom friction (Chezy, Manning) and turbulent

mixing (Smagorinsky, Prandtl mixing length, k − ε).

• Hydrostatic or non-hydrostatic.

• Many outputting (same flexibility as SWAN):

• points, curves, maps, verticals, etc.,

• many quantities: water level, velocity, discharge,

pressure, runup, friction, k, ε, etc.

• ASCII files (tables, blocks) and binary Matlab files

(blocks).

November 1, 2011 13/37


Open source, easy-to-use model

• Freely available under the GNU GPL license at Sourceforge:

http://swash.sf.net

• Easy accessible to promote ease-of-usage:

• ANSI Fortran90, fully portable on virtually all kind of

machines

• simple datastructures, easy-to-understand

• easy to install, no special libraries (except MPI)

• light and flexible, easy to maintain

• relatively quick to set up and user-friendly in operation

• The same "touch and feel" as SWAN.

November 1, 2011 14/37


Testing and validations

• Testbed: 50 well-documented analytical and laboratory tests

including propagation, runup, dam break, hydraulic jumps,

vertical mixing, etc.

• Many simple configurations:

• flumes (2DV) and basins (2DH/3D),

• bars (Beji-Battjes, Boers, Hiswa) and shoals

(Berkhoff/elliptic, circular).

• Testing of different functionalities.

• More advanced validation: conical island, rip current,

Petten, Hiswa.

November 1, 2011 15/37


Irregular wave breaking in a barred surf zone

0 5 10 15 20 25 30−0.8

−0.6

−0.4

−0.2

0

0.2

x [m]

z [m

]

1 2 3 4 5 6 7 8

• Boers (1996); wave conditions 1B and 1C.

• Depth-averaged, 1D, ∆x = 0.03 m (150 gridpoints per wave

length).

• Initial time step = 0.001 s; CFL = 0.5.

• Manning n = 0.027.

November 1, 2011 16/37


Boers 1B (Hm0=0.206 m, Tp=2.03 s)

0 10 20 300.05

0.1

0.15

0.2

0.25

x [m]

Hm

0 [m]

0 10 20 300.5

1

1.5

2

x [m]

Tm

02 [s

]

model observation

Boers 1C (Hm0=0.103 m, Tp=3.33 s)

0 10 20 300.04

0.06

0.08

0.1

0.12

0.14

x [m]

Hm

0 [m]

0 10 20 300.5

1

1.5

2

2.5

x [m]

Tm

02 [s

]

model observation

November 1, 2011 17/37


Boers 1B

0 1 20

0.002

0.004

0.006

0.008

0.01station 1

E [m

2 /Hz]

0 1 20

0.002

0.004

0.006

0.008

0.01station 2

0 1 20

2

4

6

8x 10

−3station 3

0 1 20

2

4

6

8x 10

−3station 4

0 1 20

0.5

1

1.5

2

2.5

3x 10

−3station 5

f [Hz]

E [m

2 /Hz]

0 1 20

0.5

1

1.5

2

2.5

3x 10

−3station 6

f [Hz]0 1 2

0

0.5

1

1.5

2x 10

−3station 7

f [Hz]0 1 2

0

0.5

1

1.5

2x 10

−3station 8

f [Hz]

modelobs.

November 1, 2011 18/37


Boers 1C

0 1 20

1

2

3

4

5x 10

−3station 1

E [m

2 /Hz]

0 1 20

1

2

3

4

5x 10

−3station 2

0 1 20

1

2

3

4x 10

−3station 3

0 1 20

1

2

3

4x 10

−3station 4

0 1 20

0.5

1

1.5

2

2.5

3x 10

−3station 5

f [Hz]

E [m

2 /Hz]

0 1 20

0.5

1

1.5

2

2.5

3x 10

−3station 6

f [Hz]0 1 2

0

0.5

1

1.5

2x 10

−3station 7

f [Hz]0 1 2

0

0.2

0.4

0.6

0.8

1x 10

−3station 8

f [Hz]

modelobs.

November 1, 2011 19/37


Wave transformation over a shallow foreshore

−1300 −1100 −900 −700 −500 −300 −100 0−24

−18

−12

−6

0

6

12

x [m]

z [m

]

deep mp3 bar mp5 mp6 toe

1:30

1:25

1:20

1:100

1:25

• Measurements from Van Gent and Doorn (2000).

• ∆x = 1 m (200 gridpoints per wave length).

• 2 equidistant layers.

• No bed roughness.


November 1, 2011 20/37


storm condition; Hm0 = 4.4 m, Tp = 16.2 s

0 0.1 0.2 0.30

10

20deep

E [m

2 /Hz]

modelobs

0 0.1 0.2 0.30

10

20mp3

0 0.1 0.2 0.30

5

10

15bar

E [m

2 /Hz]

0 0.1 0.2 0.30

5

10mp5

0 0.1 0.2 0.30

5

10

15mp6

f [Hz]

E [m

2 /Hz]

0 0.1 0.2 0.30

5

10

15toe

f [Hz]

November 1, 2011 21/37


Runup of solitary wave on conical island

wave gauge

wave maker

y[m]

x[m]

A A

7.2m

7.2m

0.3m

0.32m

0.5L

7.2

m

2.2m

z[m]

x[m]

00

5

10

15

20

25

30

5 10 15 20 25

0 5 10 15 20 25

-0.2

0.0

0.2

0.4

November 1, 2011 22/37


Conical island

0246

ζ [c

m]

model obs

−5

0

5

gauge 3−10

0

10

gauge 3

−5

0

5

ζ [c

m]

gauge 6−5

0

5

gauge 6−10

0

10

gauge 6

−5

0

5

ζ [c

m]

gauge 9−5

0

5

gauge 9−10

0

10

gauge 9

−5

0

5

ζ [c

m]

gauge 16−5

0

5

gauge 16−10

0

10

gauge 16

25 30 35 40−5

0

5

time [s]

ζ [c

m]

gauge 22

25 30 35 40−5

0

5

time [s]

gauge 22

25 30 35 40−10

0

10

gauge 22

time [s]

November 1, 2011 23/37


Circulation and rip current induced by bar breaks

2

4

6

8

10

12

14

16

18

0

5

10

15

20

−0.4

−0.3

−0.2

−0.1

0

0.1

x [m]

y [m]

z [m

]

November 1, 2011 24/37


Rip current (2)

• Measurements from Haller et al. (2002).

• Monochromatic, normally incident wave: H = 4.75 cm,

T = 1 s (test B).

• Depth-averaged.


• Smagorinsky subgrid model Cs = 0.1.

• ∆x = ∆y = 0.05 m (30 gridpoints per wave length).


November 1, 2011 25/37


Rip current (3)

0

2

4

6

8

H [c

m]

y = 11.23 m modelobservation

8 9 10 11 12 13 140

2

4

6

8

y = 13.68 m

H [c

m]

x [m]

November 1, 2011 26/37


Rip current (4)

−1

−0.5

0

0.5

1

setu

p [c

m]

y = 11.23 m

model observation

8 9 10 11 12 13 14−1

−0.5

0

0.5

1

y = 13.68 m

setu

p [c

m]

x [m]

November 1, 2011 27/37


Rip current (5)

−20

0

20

U [c

m/s

]

x = 14 m model observation

−20

0

20x = 13 m

U [c

m/s

]

−20

0

20x = 12.2 m

U [c

m/s

]

−20

0

20x = 11.2 m

U [c

m/s

]

6 7 8 9 10 11 12 13 14 15 16−20

0

20x = 10 m

U [c

m/s

]

y [m]

November 1, 2011 28/37


Rip current (6)

−20

0

20

V [c

m/s

]

x = 14 m model observation

−20

0

20x = 13 m

V [c

m/s

]

−20

0

20x = 12.2 m

V [c

m/s

]

−20

0

20x = 11.2 m

V [c

m/s

]

6 7 8 9 10 11 12 13 14 15 16−20

0

20x = 10 m

V [c

m/s

]

y [m]

November 1, 2011 29/37


Multi-directional waves propagating through a barred basi n

05

1015

2025

−30

−20

−10

0

10

20

30

40

−0.4

−0.3

−0.2

−0.1

0

0.1

x [m]

y [m]

z [m

]

November 1, 2011 30/37


HISWA (2)

• Dingemans (1987); case me35.

• 2D Jonswap spectrum: Hm0 = 10 cm, Tp = 1.24 s, cos4(θ).

• ∆x = 5 cm, ∆y = 3 cm.


• 2 equidistant layers.

• Smagorinsky model Cs = 0.1.


November 1, 2011 31/37


HISWA (3)

0 5 10 15 20 250

5

10

15

distance [m]

Hm

0 [cm

]

0 5 10 15 20 25−0.5

0

0.5

1

1.5

2

distance [m]

Tm

−10

[s]

SWASHobservation

0 5 10 15 20 250

5

10

15

distance [m]

Hm

0 [cm

]

0 5 10 15 20 25−0.5

0

0.5

1

1.5

2

distance [m]

Tm

−10

[s]

SWASHobservation

November 1, 2011 32/37


HISWA (4)

0 5 10 15 20 250

5

10

15

distance [m]

Hm

0 [cm

]

0 5 10 15 20 25−0.5

0

0.5

1

1.5

2

distance [m]

Tm

−10

[s]

SWASHobservation

0 5 10 15 20 250

5

10

15

distance [m]

Hm

0 [cm

]

0 5 10 15 20 25−0.5

0

0.5

1

1.5

2

distance [m]

Tm

−10

[s]

SWASHobservation

November 1, 2011 33/37


HISWA (5)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28−14

−12

−10

−8

−6

−4

−2

0

2

4

6

8

10

12

14

x [m]

y [m

]

SWASHobservation

November 1, 2011 34/37


Performance

CPU time in µsec per gridpoint/time step on comparable

processors:

simulation #proc SWASH COULWAVE FUNWAVE

Berkhoff shoal 1 3 21 60

8 0.3 3.2 −

Conical island 1 2.2 − 40

32 0.08 − −

Rip current 1 1.6 16.4 −

18 0.1 1.1 −

32 0.076 − −

November 1, 2011 35/37


Parallel efficiency - IBM Power6 cluster

5 10 15 20 25 30

5

10

15

20

25

30

number of cores

spee

dup

conical islandrip current

November 1, 2011 36/37


Further developments and plans

• Interaction with structures: (partial) reflection, transmission.

• Wind effects on wave transformation.

• Wave-induced forces on mooring ships (PhD project).

• Extension to unstructured grids.

• OpenMP, hotstarting, NetCDF, ...

• ...

November 1, 2011 37/37


http://swash.sf.net

nearshore wave-ﬂow modelling with swashnovember 1, 2011 4/37 environmental fluid mechanics section...

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