Abstract

In situations where the calculation of ocean wave propagation and impact on structures are required, fast numerical solvers are desired in order to find relevant wave events. Computational fluid dynamics (CFD)-based numerical wave tanks (NWTs) emphasize on the hydrodynamic details such as fluid–structure interaction, which make them less ideal for the event identification due to the large computational resources involved. Therefore, a computationally efficient numerical wave model is needed to identify the events both for offshore deep-water wave fields and coastal wave fields where the bathymetry and coastline variations have strong impact on wave propagation. In the current paper, a new numerical wave model is represented that solves the Laplace equation for the flow potential and the nonlinear kinematic and dynamics free surface boundary conditions. This approach requires reduced computational resources compared to CFD-based NWTs. The resulting fully nonlinear potential flow solver REEF3D::FNPF uses a σ-coordinate grid for the computations. This allows the grid to follow the irregular bottom variation with great flexibility. The free surface boundary conditions are discretized using fifth-order weighted essentially non-oscillatory (WENO) finite difference methods and the third-order total variation diminishing (TVD) Runge–Kutta scheme for time stepping. The Laplace equation for the potential is solved with Hypre’s stabilized bi-conjugated gradient solver preconditioned with geometric multi-grid. REEF3D::FNPF is fully parallelized following the domain decomposition strategy and the message passing interface (MPI) communication protocol. The numerical results agree well with the experimental measurements in all tested cases and the model proves to be efficient and accurate for both offshore and coastal conditions.

References

References
1.
Bihs
,
H.
,
Kamath
,
A.
,
Chella
,
M. A.
,
Aggarwal
,
A.
, and
Arntsen
,
Øivind A.
,
2016
, “
A New Level Set Numerical Wave Tank With Improved Density Interpolation for Complex Wave Hydrodynamics
,”
Comput. Fluids
,
140
, pp.
191
208
. 10.1016/j.compfluid.2016.09.012
2.
Kamath
,
A.
,
Bihs
,
H.
,
Alagan Chella
,
M.
, and
Arntsen
,
Øivind A.
,
2016
, “
Upstream-Cylinder and Downstream-Cylinder Influence on the Hydrodynamics of a Four-Cylinder Group
,”
J. Waterway Port Coastal Ocean Eng.
,
142
(
4
), p.
04016002
. 10.1061/(ASCE)WW.1943-5460.0000339
3.
Ong
,
M. C.
,
Kamath
,
A.
,
Bihs
,
H.
, and
Afzal
,
M. S.
,
2017
, “
Numerical Simulation of Free-Surface Waves Past Two Semi-Submerged Horizontal Circular Cylinders in Tandem
,”
Marine Struct.
,
52
, pp.
1
14
. 10.1016/j.marstruc.2016.11.002
4.
Wang
,
W.
,
Kamath
,
A.
, and
Bihs
,
H.
,
2018
, “
CFD Simulations of Multi-Directional Irregular Wave Interaction With a Large Cylinder
,”
37th International Conference on Offshore Mechanics and Arctic Engineering
,
Madrid, Spain
,
June 17–22
.
5.
Ahmad
,
N.
,
Bihs
,
H.
,
Myrhaug
,
D.
,
Kamath
,
A.
, and
Arntsen
,
Øivind A.
,
2018
, “
Three-Dimensional Numerical Modelling of Wave-Induced Scour Around Piles in a Side-By-Side Arrangement
,”
Coastal Eng.
,
138
, pp.
132
151
. 10.1016/j.coastaleng.2018.04.016
6.
Sasikumar
,
A.
,
Kamath
,
A.
,
Musch
,
O.
,
Bihs
,
H.
, and
Arntsen
,
Ø. A.
,
2018
, “
Numerical Modeling of Berm Breakwater Optimization With Varying Berm Geometry Using REEF3D
,”
ASME J. Offshore Mech. Arct. Eng.
,
141
(
1
), p.
011801
. 10.1115/1.4040508
7.
Madsen
,
P. A.
,
Murray
,
R.
, and
Sørensen
,
O. R.
,
1991
, “
A New Form of the Boussinesq Equations With Improved Linear Dispersion Characteristics
,”
Coastal Eng.
,
15
, pp.
371
388
. 10.1016/0378-3839(91)90017-B
8.
Nwogu
,
O.
,
1993
, “
Alternative Form of Boussinesq Equations for Nearshore Wave Propagation
,”
J. Waterways Port Coastal Ocean Eng.
,
119
(
6
), pp.
618
638
. 10.1061/(ASCE)0733-950X(1993)119:6(618)
9.
Ducrozet
,
G.
,
Bonnefoy
,
F.
,
Le Touzé
,
D.
, and
Ferrant
,
P.
,
2012
, “
A Modified High-Order Spectral Method for Wavemaker Modeling in a Numerical Wave Tank
,”
Eur. J. Mech. B/Fluids
,
34
, pp.
19
34
. 10.1016/j.euromechflu.2012.01.017
10.
Ducrozet
,
G.
,
Bonnefoy
,
F.
,
Le Touzé
,
D.
, and
Ferrant
,
P.
,
2016
, “
HOS-Ocean: Open-Source Solver for Nonlinear Waves in Open Ocean Based on High-Order Spectral Method
,”
Comput. Phys. Commun.
,
203
, pp.
245
254
. 10.1016/j.cpc.2016.02.017
11.
Grilli
,
S.
,
1996
, “
Fully Nonlinear Potential Flow Models Used for Long Wave Runup Prediction
,”
Long-Wave Runup Models
,
New Jersey
.
12.
Li
,
B.
, and
Fleming
,
C. A.
,
1997
, “
A Three Dimensional Multigrid Model for Fully Nonlinear Water Waves
,”
Coastal Engineering
,
30
, pp.
235
258
.
13.
Bingham
,
H. B.
, and
Zhang
,
H.
,
2007
, “
On the Accuracy of Finite-Difference Solutions for Nonlinear Water Waves
,”
J. Eng. Math.
,
58
(
1–4
), pp.
211
228
.
14.
Engsig-Karup
,
A.
,
Bingham
,
H.
, and
Lindberg
,
O.
,
2009
, “
An Efficient Flexible-Order Model for 3D Nonlinear Water Waves
,”
J. Comput. Phys.
,
228
, pp.
2100
2118
. 10.1016/j.jcp.2008.11.028
15.
Engsig-Karup
,
A.
, and
Bingham
,
H.
,
2009
, “
Boundary-Fitted Solutions for 3d Nonlinear Water Wave-Structure Interaction
,”
24th International Workshop on Water Waves and Floating Bodies
,
Zelenogorsk, Russian Federation
,
Apr. 19–22
, p.
20
.
16.
Ducrozet
,
G.
,
Engsig-Karup
,
A. P.
,
Bingham
,
H. B.
, and
Ferrant
,
P.
,
2014
, “
A Non-Linear Wave Decomposition Model for Efficient Wave–Structure Interaction. Part A: Formulation, Validations and Analysis
,”
J. Comput. Phys.
,
257
, pp.
863
883
. 10.1016/j.jcp.2013.09.017
17.
Janssen
,
C. F.
,
Grilli
,
T.
, and
Krafczyk
,
M.
,
2010
, “
Modeling of Wave Breaking and Wave–Structure Interactions by Coupling of Fully Nonlinear Potential Flow and Lattice-Boltzmann Models
,”
The Twentieth International Offshore and Polar Engineering Conference
,
Beijing, China
,
June 20–25
.
18.
Mehmood
,
A.
,
Graham
,
D. I.
,
Langfeld
,
K.
, and
Greaves
,
D. M.
,
2015
, “
OpenFOAM Finite Volume Method Implementation of a Fully Nonlinear Potential Flow Model for Simulating Wave-Structure Interactions
,”
The Twenty-fifth International Ocean and Polar Engineering Conference
,
Kona, HI
,
June 21–26
.
19.
Mehmood
,
A.
,
Graham
,
D. I.
,
Langfeld
,
K.
, and
Greaves
,
D. M.
,
2016
, “
Numerical Simulation of Nonlinear Water Waves Based on Fully Nonlinear Potential Flow Theory in OpenFOAM®-Extend
,”
The 26th International Ocean and Polar Engineering Conference
,
Rhodes, Greece
,
June 26–July 2
.
20.
Engsig-Karup
,
A. P.
,
Madsen
,
M. G.
, and
Glimberg
,
S. L.
,
2012
, “
A Massively Parallel GPU-Accelerated Model for Analysis of Fully Nonlinear Free Surface Waves
,”
Int. J. Numer. Methods Fluids
,
70
(
1
), pp.
20
36
.
21.
Engsig-Karup
,
A. P.
,
Glimberg
,
S. L.
,
Nielsen
,
A. S.
, and
Lindberg
,
O.
,
2013
,
Fast Hydrodynamics on Heterogenous Many-Core Hardware
,
Taylor & Francis
,
London
, pp.
251
294
.
22.
Glimberg
,
L. S.
,
Engsig-Karup
,
A. P.
,
Nielsen
,
A. S.
, and
Dammann
,
B.
,
2013
, “In Designing Scientific Applications on GPUs,”
Development of Software Components for Heterogeneous Many-Core Architectures
,
R.
Couturier
, ed.,
CRC Press/Taylor & Francis Group
,
Halmstad
, pp.
73
104
.
23.
Mayer
,
S.
,
Garapon
,
A.
, and
Sørensen
,
L. S.
,
1998
, “
A Fractional Step Method for Unsteady Free Surface Flow With Applications to Non-Linear Wave Dynamics
,”
Int. J. Numer. Methods Fluids
,
28
(
2
), pp.
293
315
. 10.1002/(SICI)1097-0363(19980815)28:2<293::AID-FLD719>3.0.CO;2-1
24.
Jacobsen
,
N. G.
,
Fuhrman
,
D. R.
, and
Fredsøe
,
J.
,
2012
, “
A Wave Generation Toolbox for the Open-Source CFD Library: OpenFOAM
,”
Int. J. Numer. Methods Fluids
,
70
(
9
), pp.
1073
1088
. 10.1002/fld.2726
25.
van der Vorst
,
H.
,
1992
, “
BiCGStab: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
,”
SIAM J. Sci. Comput.
,
13
(
2
), pp.
631
644
. 10.1137/0913035
26.
Jiang
,
G. S.
, and
Shu
,
C. W.
,
1996
, “
Efficient Implementation of Weighted ENO Schemes
,”
J. Comput. Phys.
,
126
, pp.
202
228
. 10.1006/jcph.1996.0130
27.
Shu
,
C. W.
, and
Osher
,
S.
,
1988
, “
Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes
,”
J. Comput. Phys.
,
77
, pp.
439
471
. 10.1016/0021-9991(88)90177-5
28.
Beji
,
S.
, and
Battjes
,
J. A.
,
1993
, “
Experimental Investigation of Wave Propagation Over a Bar
,”
Coastal Eng.
,
19
, pp.
151
162
. 10.1016/0378-3839(93)90022-Z
29.
Clauss
,
G. F.
, and
Steinhagen
,
U.
,
1999
, “
Numerical Simulation of Nonlinear Transient Waves and Its Validation by Laboratory Data
,”
9th International Offshore and Polar Engineering Conference
,
Brest, France
,
May 30–June 4
.
30.
Bihs
,
H.
,
Kamath
,
A.
,
Alagan Chella
,
M.
, and
Arntsen
,
Ø. A.
,
2019
, “
Extreme Wave Generation, Breaking, and Impact Simulations Using Wave Packets in REEF3D
,”
ASME J. Offshore Mech. Arct. Eng.
,
141
(
4
), p.
041802
. 10.1115/1.4042178
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