Nearshore wave-flow modelling
with SWASH
12th Waves Workshop
Marcel, Guus and Pieter
November 1, 2011
1/37
Environmental Fluid Mechanics Section
Delft University of Technology
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
Environmental Fluid Mechanics Section
2/37
Methodology
• The simplest modelling for wave transformation is the nonlinear
shallow water (NLSW) equations.
• NLSW-type models exhibit conservation properties and are able
to deal with breaking/bore capturing, dike breach flooding, and
tsunami inundation, among others.
• With the inclusion of non-hydrostatic pressure, many other wave
phenomena (dispersion, surf beat, triads, etc.) can be described
in a natural manner as well.
• Water depth can be divided into a number of layers and thereby
take into account vertical variation (e.g. undertow).
• Also, they improve their frequency dispersion by increasing the
number of layers.
November 1, 2011
Environmental Fluid Mechanics Section
3/37
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
Environmental Fluid Mechanics Section
4/37
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
Environmental Fluid Mechanics Section
5/37
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
Environmental Fluid Mechanics Section
6/37
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
Environmental Fluid Mechanics Section
7/37
− 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
Environmental Fluid Mechanics Section
8/37
− 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
Environmental Fluid Mechanics Section
9/37
General layer concept
November 1, 2011
Environmental Fluid Mechanics Section
10/37
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
Environmental Fluid Mechanics Section
11/37
− 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
Environmental Fluid Mechanics Section
12/37
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
Environmental Fluid Mechanics Section
13/37
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
Environmental Fluid Mechanics Section
14/37
Irregular wave breaking in a barred surf zone
0.2
1
2
5
10
3
4
5
6
7
8
z [m]
0
−0.2
−0.4
−0.6
−0.8
0
15
x [m]
20
25
30
• 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
Environmental Fluid Mechanics Section
15/37
Boers 1B (Hm0 =0.206 m, Tp =2.03 s)
2
0.2
Tm02 [s]
H
m0
[m]
0.25
0.15
0.1
1.5
1
model
0.05
0
10
20
0.5
30
0
observation
10
x [m]
20
30
x [m]
0.14
2.5
0.12
2
Tm02 [s]
H
m0
[m]
Boers 1C (Hm0 =0.103 m, Tp =3.33 s)
0.1
0.08
0.06
0.04
1.5
1
model
0
10
20
x [m]
November 1, 2011
Environmental Fluid Mechanics Section
30
0.5
0
observation
10
20
30
x [m]
16/37
Boers 1B
station 2
0.01
0.01
0.008
0.008
0.006
0.006
8
2
E [m /Hz]
station 1
0.004
0.004
0.002
0.002
0
2
E [m /Hz]
3
0
1
2
−3
station
5
x 10
0
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
1
f [Hz]
2
0
0
1
2
−3
station
6
x 10
−3
station
3
x 10
8
6
6
4
4
2
2
0
2
0
1
2
−3
station
7
x 10
0
2
−3
station
4
x 10
0
1
2
−3
station
8
x 10
model
obs.
0
1
f [Hz]
November 1, 2011
Environmental Fluid Mechanics Section
2
1.5
1.5
1
1
0.5
0.5
0
0
1
f [Hz]
2
0
0
1
2
f [Hz]
17/37
Boers 1C
5
4
4
3
3
−3
x 10station 2
4
2
E [m /Hz]
5
−3
x 10station 1
2
2
1
1
0
3
0
1
2
−3
x 10station 5
0
3
2.5
0
1
2
−3
x 10station 6
−3
x 10station 3
4
3
3
2
2
1
1
0
2
0
1
2
−3
x 10station 7
1
2.5
2
E [m /Hz]
0
1
2
−3
x 10station 8
model
obs.
0.8
1.5
2
0
−3
x 10station 4
2
0.6
1.5
1.5
1
1
0.5
0.5
1
0.4
0.5
0
0
1
f [Hz]
2
0
0
1
f [Hz]
November 1, 2011
Environmental Fluid Mechanics Section
2
0
0.2
0
1
f [Hz]
2
0
0
1
2
f [Hz]
18/37
Wave transformation over a shallow foreshore
12
6 deep
mp3
bar
mp5
mp6 toe
1:25
z [m]
0
1:25
−6
1:100
1:20
1:30
−12
−18
−24
−1300
−1100
−900
−700
x [m]
−500
−300
−100
0
• Measurements from Van Gent and Doorn (2000).
• ∆x = 1 m (200 gridpoints per wave length).
• 2 equidistant layers.
• No bed roughness.
• Initial time step = 0.02 s; CFL = 0.5.
November 1, 2011
Environmental Fluid Mechanics Section
19/37
storm condition; Hm0 = 4.4 m, Tp = 16.2 s
deep
mp3
2
E [m /Hz]
20
20
model
obs
10
0
10
0
0.1
0.2
0.3
0
0
0.1
bar
0.2
0.3
0.2
0.3
10
10
2
E [m /Hz]
0.3
mp5
15
5
5
0
0
0.1
0.2
0.3
0
0
0.1
mp6
toe
15
15
10
10
5
5
2
E [m /Hz]
0.2
0
0
0.1
0.2
f [Hz]
November 1, 2011
Environmental Fluid Mechanics Section
0.3
0
0
0.1
f [Hz]
20/37
Runup of solitary wave on conical island
30
wave gauge
25
wave maker
20
7.2m
y[m]
15
A
A
10
5
0
0.5L
0
5
7.2m
10
15
20
25
15
20
25
x[m]
0.4
z[m]
2.2m
0.2
0.3m
0.0
0.32m
-0.2
7.2m
0
5
10
x[m]
November 1, 2011
Environmental Fluid Mechanics Section
21/37
ζ [cm]
ζ [cm]
Conical island
6
4
2
0
model
5
10
0
0
obs
gauge 3
−10
5
5
10
0
0
0
ζ [cm]
gauge 6
gauge 6
ζ [cm]
gauge 6
−5
−5
−10
5
5
10
0
0
0
gauge 9
gauge 9
gauge 9
−5
−5
−10
5
5
10
0
0
0
gauge 16
ζ [cm]
gauge 3
−5
gauge 16
gauge 16
−5
−5
−10
5
5
10
0
0
0
gauge 22
gauge 22
−5
25
30
35
time [s]
40
−5
25
November 1, 2011
Environmental Fluid Mechanics Section
30
35
time [s]
gauge 22
40
−10
25
30
35
time [s]
40
22/37
Circulation and rip current induced by bar breaks
0.1
z [m]
0
−0.1
−0.2
18
16
−0.3
14
−0.4
12
20
10
15
8
10
6
4
5
y [m]
November 1, 2011
Environmental Fluid Mechanics Section
0
2
x [m]
23/37
Rip current (2)
• Measurements from Haller et al. (2002).
• Monochromatic, normally incident wave: H = 4.75 cm,
T = 1 s (test B).
• Depth-averaged.
• Manning n = 0.019.
• Smagorinsky subgrid model Cs = 0.1.
• ∆x = ∆y = 0.05 m (30 gridpoints per wave length).
• Initial time step = 0.005 s; CFL = 0.5.
November 1, 2011
Environmental Fluid Mechanics Section
24/37
Rip current (3)
8
model
observation
y = 11.23 m
H [cm]
6
4
2
0
8
y = 13.68 m
H [cm]
6
4
2
0
8
9
10
11
12
13
14
x [m]
November 1, 2011
Environmental Fluid Mechanics Section
25/37
Rip current (4)
1
y = 11.23 m
setup [cm]
0.5
0
−0.5
model
observation
−1
1
y = 13.68 m
setup [cm]
0.5
0
−0.5
−1
8
9
10
11
12
13
14
x [m]
November 1, 2011
Environmental Fluid Mechanics Section
26/37
U [cm/s]
U [cm/s]
U [cm/s]
U [cm/s]
U [cm/s]
Rip current (5)
20
x = 14 m
model
0
observation
−20
20
x = 13 m
0
−20
20
x = 12.2 m
0
−20
20
x = 11.2 m
0
−20
20
x = 10 m
0
−20
6
7
8
9
10
11
12
13
14
15
16
y [m]
November 1, 2011
Environmental Fluid Mechanics Section
27/37
V [cm/s]
V [cm/s]
V [cm/s]
V [cm/s]
V [cm/s]
Rip current (6)
20
x = 14 m
0
model
observation
−20
20
x = 13 m
0
−20
20
x = 12.2 m
0
−20
20
x = 11.2 m
0
−20
20
x = 10 m
0
−20
6
7
8
9
10
11
12
13
14
15
16
y [m]
November 1, 2011
Environmental Fluid Mechanics Section
28/37
Multi-directional waves propagating through a barred basin
0.1
0
z [m]
−0.1
−0.2
−0.3
−0.4
−30
−20
−10
0
10
0
20
5
10
30
y [m]
15
40
20
25
November 1, 2011
Environmental Fluid Mechanics Section
x [m]
29/37
HISWA (2)
• Dingemans (1987); case me35.
• 2D Jonswap spectrum: Hm0 = 10 cm, Tp = 1.24 s, cos4 (θ).
• ∆x = 5 cm, ∆y = 3 cm.
• Initial time step = 0.005 s; CFL = 0.7.
• 2 equidistant layers.
• Smagorinsky model Cs = 0.1.
• Manning n = 0.02.
November 1, 2011
Environmental Fluid Mechanics Section
30/37
HISWA (3)
15
2
[s]
m−10
10
5
T
Hm0 [cm]
1.5
1
0.5
SWASH
observation
0
0
0
5
10
15
distance [m]
20
−0.5
25
15
0
5
10
15
distance [m]
20
25
20
25
2
[s]
m−10
10
5
T
Hm0 [cm]
1.5
1
0.5
SWASH
observation
0
0
0
5
10
15
distance [m]
20
November 1, 2011
Environmental Fluid Mechanics Section
25
−0.5
0
5
10
15
distance [m]
31/37
HISWA (4)
15
2
[s]
m−10
10
5
T
Hm0 [cm]
1.5
1
0.5
SWASH
observation
0
0
0
5
10
15
distance [m]
20
−0.5
25
15
0
5
10
15
distance [m]
20
25
20
25
2
[s]
m−10
10
5
T
Hm0 [cm]
1.5
1
0.5
SWASH
observation
0
0
0
5
10
15
distance [m]
20
November 1, 2011
Environmental Fluid Mechanics Section
25
−0.5
0
5
10
15
distance [m]
32/37
HISWA (5)
14
12
10
8
6
4
y [m]
2
0
−2
−4
−6
−8
−10
−12
−14
SWASH
observation
0
2
4
6
8
10
November 1, 2011
Environmental Fluid Mechanics Section
12
14
x [m]
16
18
20
22
24
26
28
33/37
Performance
CPU time in µsec per gridpoint/time step on comparable
processors:
simulation
Berkhoff shoal
Conical island
Rip current
#proc
SWASH
COULWAVE
FUNWAVE
1
3
21
60
8
0.3
3.2
−
1
2.2
−
40
32
0.08
−
−
1
1.6
16.4
−
18
0.1
1.1
−
32
0.076
−
−
November 1, 2011
Environmental Fluid Mechanics Section
34/37
Parallel efficiency - IBM Power6 cluster
30
speedup
25
20
15
10
5
conical island
rip current
5
10
15
20
25
30
number of cores
November 1, 2011
Environmental Fluid Mechanics Section
35/37
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
Environmental Fluid Mechanics Section
36/37
http://swash.sf.net
November 1, 2011
Environmental Fluid Mechanics Section
37/37