For the estimation of wave loads on offshore structures, relevant extreme wave events need to be identified. In order to achieve this, long-term wave simulations of relatively large scales need to be performed. Computational fluid dynamics (CFD) based numerical wave tanks with an interface capturing two-phase flow approach typically require too large computational resources. In this paper, a three-dimensional (3D) nonhydrostatic wave model is presented, which solves the Navier–Stokes equations and employs an interface tracking method based on the continuity of the horizontal velocities along the vertical water column. With this approach, relatively fewer cells are needed in the vicinity of the air–water interface compared to CFD-based numerical wave tanks. The numerical model solves the governing equations on a rectilinear grid, which allows for the employment of high-order finite differences. The capabilities of the new wave model are presented by comparing the wave propagation in the tank with the CFD approach in a two-dimensional (2D) simulation. Further, a 3D simulation is carried out to determine the wave forces on a vertical cylinder. The calculated wave forces using the new approach are compared to those obtained using the CFD approach and experimental data. It is seen that the new approach provides a similar accuracy to that from the CFD approach while providing a large reduction in the time taken for the simulation. The gain is calculated to be about 4.5 for the 2D simulation and about 7.1 for the 3D simulation.

References

References
1.
Kamath
,
A.
,
Alagan Chella
,
M.
,
Bihs
,
H.
, and
Arntsen
,
Ø. A.
,
2015
, “
CFD Investigations of Wave Interaction With a Pair of Large Tandem Cylinders
,”
Ocean Eng.
,
108
, pp.
738
748
.
2.
Kamath
,
A.
,
Bihs
,
H.
,
Alagan Chella
,
M.
, and
Arntsen
,
Ø. A.
,
2016
, “
Upstream-Cylinder and Downstream-Cylinder Influence on the Hydrodynamics of a Four-Cylinder Group
,”
J. Waterw., Port, Coastal, Ocean Eng.
,
142
(
4
), p.
04016002
.https://ascelibrary.org/doi/10.1061/%28ASCE%29WW.1943-5460.0000339
3.
Kamath
,
A.
,
Alagan Chella
,
M.
,
Bihs
,
H.
, and
Arntsen
,
Ø. A.
,
2015
, “
Evaluating Wave Forces on Groups of Three and Nine Cylinders Using a 3D Numerical Wave Tank
,”
Eng. Appl. Comput. Fluid Mech.
,
9
(
1
), pp.
343
354
.
4.
Kamath
,
A.
,
Alagan Chella
,
M.
,
Bihs
,
H.
, and
Arntsen
,
Ø. A.
,
2016
, “
Breaking Wave Interaction With a Vertical Cylinder and the Effect of Breaker Location
,”
Ocean Eng.
,
128
, pp.
105
115
.
5.
Bihs
,
H.
,
Kamath
,
A.
,
Alagan Chella
,
M.
, and
Arntsen
,
Ø. A.
,
2016
, “
Breaking-Wave Interaction With Tandem Cylinders Under Different Impact Scenarios
,”
J. Waterw., Port, Coastal, Ocean Eng.
,
142
(
5
), p.
04016005
.https://ascelibrary.org/doi/10.1061/%28ASCE%29WW.1943-5460.0000343
6.
Alagan Chella
,
M.
,
Bihs
,
H.
,
Myrhaug
,
D.
, and
Muskulus
,
M.
,
2017
, “
Breaking Solitary Waves and Breaking Wave Forces on a Vertically Mounted Slender Cylinder Over an Impermeable Sloping Seabed
,”
J. Ocean Eng. Mar. Energy
,
3
(
1
), pp.
1
19
.
7.
Bihs
,
H.
,
Alagan Chella
,
M.
,
Kamath
,
A.
, and
Arntsen
,
Ø. A.
,
2017
, “
Numerical Investigation of Focused Waves and Their Interaction With a Vertical Cylinder Using REEF3D
,”
ASME J. Offshore Mech. Arct. Eng.
,
139
(
4
), p.
041101
.
8.
Bihs
,
H.
,
Kamath
,
A.
,
Alagan Chella
,
M.
, and
Arntsen
,
Ø. A.
,
2017
, “
Extreme Wave Generation, Breaking and Impact Simulations With REEF3D
,”
ASME
Paper No. OMAE2017-61524.
9.
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.
Higuera
,
P.
,
Lara
,
L. J.
, and
Losada
,
I. J.
,
2013
, “
Realistic Wave Generation and Active Wave Absorption for Navier-Stokes Models Application to OpenFOAM
,”
Coastal Eng.
,
71
, pp.
102
118
.
11.
Stelling
,
G.
, and
Zijlema
,
M.
,
2003
, “
An Accurate and Efficient Finite-Difference Algorithm for Non-Hydrostatic Free-Surface Flow With Application to Wave Propagation
,”
Int. J. Numer. Methods Fluids
,
43
(
1
), pp.
1
23
.
12.
Zijlema
,
M.
,
Stelling
,
G.
, and
Smit
,
P.
,
2005
, “
Further Experiences With Computing Non-Hydrostatic Free-Surface Flows Involving Water Waves
,”
Int. J. Numer. Methods Fluids
,
48
(
2
), pp.
169
197
.
13.
Zijlema
,
M.
, and
Stelling
,
G.
,
2008
, “
Efficient Computation of Surf Zone Waves Using the Nonlinear Shallow Water Equations With Non-Hydrostatic Pressure
,”
Coastal Eng.
,
55
(
10
), pp.
780
790
.
14.
Ma
,
G.
,
Shi
,
F.
, and
Kirby
,
J. T.
,
2012
, “
Shock-Capturing Non-Hydrostatic Model for Fully Dispersive Surface Wave Processes
,”
Ocean Model.
,
43–44
, pp.
22
35
.
15.
Ma
,
G.
,
Farahani
,
A. A.
,
Kirby
,
J. T.
, and
Shi
,
F.
,
2016
, “
Modeling Wave-Structure Interactions by an Immersed Boundary Method in a σ-Coordinate Model
,”
Ocean Eng.
,
125
, pp.
238
247
.
16.
Young
,
C.-C.
, and
Wu
,
C. H.
,
2010
, “
A σ-Coordinate Non-Hydrostatic Model With Embedded Boussinesq-Type-Like Equations for Modeling Deep-Water Waves
,”
Int. J. Numer. Methods Fluids
,
63
(
12
), pp.
1448
1470
.
17.
Choi
,
D. Y.
,
Wu
,
C. H.
, and
Young
,
C.-C.
,
2011
, “
An Efficient Curvilinear Non-Hydrostatic Model for Simulating Surface Water Waves
,”
Int. J. Numer. Methods Fluids
,
66
(
9
), pp.
1093
1115
.
18.
Ai
,
C.
,
Jin
,
S.
, and
Lv
,
B.
,
2011
, “
A New Fully Non-Hydrostatic 3D Free Surface Flow Model for Water Wave Motions
,”
Int. J. Numer. Methods Fluids
,
66
(
11
), pp.
1354
1370
.
19.
Ai
,
C.
,
Ding
,
W.
, and
Jin
,
S.
,
2014
, “
A General Boundary-Fitted 3D Non-Hydrostatic Model for Nonlinear Focusing Wave Groups
,”
Ocean Eng.
,
89
, pp.
134
145
.
20.
Stelling
,
S. G.
, and
Van Kester
,
J. A. T. M.
,
1994
, “
On the Approximation of Horizontal Gradients in Sigma Co-Ordinates for Bathymetry With Steep Bottom Slopes
,”
Int. J. Numer. Methods Fluids
,
18
(
10
), pp.
915
935
.
21.
Bihs
,
H.
,
Kamath
,
A.
,
Alagan Chella
,
M.
,
Aggarwal
,
A.
, and
Arntsen
,
Ø. A.
,
2016
, “
A New Level Set Numerical Wave Tank With Improved Density Interpolation for Complex Wave Hydrodynamics
,”
Comput. Fluids
,
140
, pp.
191
208
.
22.
Bihs
,
H.
, and
Kamath
,
A.
,
2017
, “
Simulation of Floating Bodies With a Combined Level Set/Ghost Cell Immersed Boundary Representation
,”
Int. J. Numer. Methods Fluids
,
83
(
12
), pp.
905
916
.
23.
Chen
,
L. F.
,
Zang
,
J.
,
Hillis
,
A. J.
,
Morgan
,
G. C. J.
, and
Plummer
,
A. R.
,
2014
, “
Numerical Investigation of Wave–Structure Interaction Using OpenFOAM
,”
Ocean Eng.
,
88
, pp.
91
109
.
24.
Chorin
,
A.
,
1968
, “
Numerical Solution of the Navier-Stokes Equations
,”
Math. Comput.
,
22
(
104
), pp.
745
762
.
25.
Falgout
,
R.
,
Cleary
,
A.
,
Jones
,
J.
,
Chow
,
E.
,
Henson
,
V.
,
Baldwin
,
C.
,
Brown
,
P.
,
Vassilevski
,
P.
, and
Yang
,
U.
,
2010
, “HYPRE: High Performance Preconditioners, User's Manual, Ver. 2.11,”
Center for Applied Scientific Computing, Lawrence Livermore National Laboratory
,
Livermore, CA
.
26.
Ashby
,
S. F.
, and
Falgout
,
R. D.
,
1996
, “
A Parallel Multigrid Preconditioned Conjugate Gradient Algorithm for Groundwater Flow Simulations
,”
Nucl. Sci. Eng.
,
124
(
1
), pp.
145
159
.
27.
Wilcox
,
D. C.
,
1994
,
Turbulence Modeling for CFD
,
DCW Industries
,
La Canada, CA
.
28.
Durbin
,
P. A.
,
2009
, “
Limiters and Wall Treatments in Applied Turbulence Modeling
,”
Fluid Dyn. Res.
,
41
(
1
), pp.
1
18
.
29.
Naot
,
D.
, and
Rodi
,
W.
,
1982
, “
Calculation of Secondary Currents in Channel Flow
,”
J. Hydraulic Div., ASCE
,
108
(
8
), pp.
948
968
.https://cedb.asce.org/CEDBsearch/record.jsp?dockey=0034501
30.
Jiang
,
G. S.
, and
Shu
,
C. W.
,
1996
, “
Efficient Implementation of Weighted ENO Schemes
,”
J. Comput. Phys.
,
126
(
1
), pp.
202
228
.
31.
Harten
,
A.
,
1983
, “
High Resolution Schemes for Hyperbolic Conservation Laws
,”
J. Comput. Phys.
,
49
(
3
), pp.
357
393
.
32.
Peskin
,
C. S.
,
1972
, “
Flow Patterns Around the Heart Valves
,”
J. Comput. Phys.
,
10
(
2
), pp.
252
271
.
33.
Berthelsen
,
P. A.
, and
Faltinsen
,
O. M.
,
2008
, “
A Local Directional Ghost Cell Approach for Incompressible Viscous Flow Problems With Irregular Boundaries
,”
J. Comput. Phys.
,
227
(
9
), pp.
4354
4397
.
34.
Engsig-Karup
,
A. P.
,
2006
, “
Unstructured Nodal DG-FEM Solution of High-Order Boussinesq-Type Equations
,”
Ph.D. thesis
, Technical University of Denmark, Lyngby, Denmark.http://orbit.dtu.dk/en/publications/unstructured-nodal-dgfem-solution-of-highorder-boussinesqtype-equations(52502078-1608-4799-8e55-41f60bb92db6).html
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