In recent decades, the use of computational fluid dynamics (CFD) in many areas of engineering as a research and development tool has seen remarkable growth. Recently, an increasing concern with the assessment of the quality of CFD results has been observed. Wave modeling is an important task in many ocean engineering applications. Although numerical modeling studies of waves can be found in the literature for many applications, it is hard to find studies that present the numerical uncertainties of the results. In this study, the numerical uncertainties in mean wave parameters simulated using a viscous model were estimated using a procedure based on grid/time refinement studies and power series expansions. starccm+ software was used to simulate wave propagation. The computational domain was discretized using a trimmer mesh. The results obtained for a regular wave with a wave steepness (H/L) equal to 0.025 are presented. The numerical uncertainties in mean wave height and mean wave period were estimated along the computational domain. The results indicate that the convergence properties of the mean wave parameters with the grid refinement depended on both position in the domain and the selected wave parameter.

References

References
1.
ASME
,
2009
, “Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer,” American Society of Mechanical Engineers, New York, Standard No.
ASME-V&V20
.
2.
Oberkampf
,
W.
, and
Roy
,
C.
,
2010
,
Verification and Validation in Scientific Computing
,
1st ed.
,
Cambridge University Press
,
Cambridge, UK
, p.
790
.
3.
Richardson
,
L. F.
,
1911
, “
The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, With an Application to the Stresses in a Masonry Dam
,”
Philos. Trans. R. Soc. London A
,
210
(
459–470
), pp.
307
357
.
4.
Richardson
,
L. F.
, and
Gaunt
,
J. A.
,
1927
, “
The Deferred Approach to the Limit
,”
Philos. Trans. R. Soc. London A
,
226
(
636–646
), pp.
299
361
.
5.
Roache
,
P.
,
1994
, “
Perspective: A Method for Uniform Reporting of Grid Refinement Studies
,”
ASME J. Fluids Eng.
,
116
(
3
), pp.
405
413
.
6.
Eça
,
L.
, and
Hoekstra
,
M.
,
2014
, “
A Procedure for the Estimation of the Numerical Uncertainty of CFD Calculations Based on Grid Refinement Studies
,”
J. Comput. Phys.
,
262
(
1
), pp.
104
130
.
7.
Wilson
,
R. V.
,
Stern
,
F.
,
Coleman
,
H. W.
, and
Paterson
,
E. G.
,
2001
, “
Comprehensive Approach to Verification and Validation of CFD Simulations—Part 2: Application for RANS Simulation of a Cargo/Container Ship
,”
ASME J. Fluids Eng.
,
123
(
4
), pp.
803
810
.
8.
Toxopeus
,
S.
, and
Vaz
,
G.
,
2009
, “Calculation of Current or Manoeuvering Forces Using Viscous-Flow Solver,”
ASME
Paper No. OMAE2009-79782.
9.
Toxopeus
,
S. L.
,
2011
, “Practical Application of Viscous-Flow Calculations for the Simulation of Manoeuvring Ships,”
Ph.D. thesis
, Delft University of Technology, Wageningen, The Netherlands, p.
238
.
10.
Koop
,
A. H.
,
Klaij
,
C. M.
, and
Vaz
,
G.
,
2013
, “
Viscous-Flow Calculations for Model and Full-Scale Current Loads on Typical Offshore Structures
,” MARINE 2011, IV International Conference on Computational Methods in Marine Engineering (Computational Methods in Applied Sciences, Vol. 29), L. Eça, E. Onate, J. García-Espinosa, T. Kvamsdal, and P. Bergan, eds., Springer, Dordrecht, The Netherlands, pp.
3
29.
11.
Koop
,
A.
,
2016
, “Determining Side-by-Side Current Loads Using CFD and Model Tests,”
ASME
Paper No. OMAE2016-54344.
12.
Maguire
,
A.
, and
Ingram
,
D.
,
2009
, “
Hydrodynamics and Absorption Efficiencies of Wavemakers
,”
Eighth European Wave and Tidal Energy Conference
, Uppsala, Sweden, Sept. 7–10, pp.
859
868
.
13.
Wu
,
G.
, and
Oakley
,
O. H.
,
2009
, “CFD Modeling of Fully Nonlinear Water Wave Tank,”
ASME
Paper No. OMAE2009-80012.
14.
Silva
,
M.
,
Araujo
,
M.
,
Pinto
,
W.
, and
Levi
,
C.
,
2010
, “
Numerical Simulation of Monochromatic Wave Generated in Laboratory: Validation of a CFD Code
,”
23°Congresso Nacional De Transporte Aquaviário, Construção Naval e Offshore
, Rio de Janeiro, Brazil, Oct. 25–29, Paper No. SOBENA2010-141.
15.
Maguire
,
A. E.
,
2011
, “Hydrodynamics, Control and Numerical Modelling of Absorbing Wavemakers,”
Ph.D. thesis
, The University of Edinburgh, Edinburgh, UK.
16.
Silva
,
M.
,
Vitola
,
M.
,
Pinto
,
W.
, and
Levi
,
C.
,
2012
, “Numerical Simulations of Regular Waves in a Hydrodynamic Laboratory Basin,”
ASME
Paper No. OMAE2012-83830.
17.
Finnegan
,
W.
, and
Goggins
,
J.
,
2012
, “
Numerical Simulation of Linear Water Waves and Wave-Structure Interaction
,”
Ocean Eng.
,
43
, pp.
23
31
.
18.
Anbarsooz
,
M.
,
Passandideh-Fard
,
M.
, and
Moghiman
,
M.
,
2013
, “
Fully Nonlinear Viscous Wave Generation in Numerical Wave Tanks
,”
Ocean Eng.
,
59
, pp.
73
85
.
19.
Fathi
,
F.
,
Eça
,
L.
, and
Borsboom
,
M.
,
2011
, “An Example of Code Verification in the Simulation of Wave Propagation,”
ASME
Paper No. OMAE2011-49398.
20.
Eça
,
L.
,
Vaz
,
G.
, and
Hoekstra
,
M.
,
2010
, “Code Verification, Solution Verification and Validation in RANS Solvers,”
ASME
Paper No. OMAE2010-20338.
21.
Eça
,
L.
,
Vaz
,
G.
, and
Hoekstra
,
M.
,
2014
, “Code Verification of ReFRESCO With a Statistically Periodic Manufactured Solution,”
ASME
Paper No. OMAE2014-23258.
22.
Saad
,
Y.
,
2003
,
Iterative Methods for Sparse Linear Systems
,
2nd ed.
,
Society for Industrial and Applied Mathematics
,
Philadelphia, PA
, p.
528
.
23.
Perić
,
M.
,
Kressler
,
R.
, and
Scheuerer
,
G.
,
1988
, “
Comparison of Finite Volume Numerical Methods With Staggered and Colocated Grids
,”
Comput. Fluids
,
16
(
4
), pp.
389
403
.
24.
Muzaferija
,
S.
, and
Perić
,
M.
,
1999
, “
Computational of Free Surface Flows Using Interface-Tracking and Interface-Capturing Methods
,”
Nonlinear Water Wave Interaction
(Advances in Fluid Mechanics), O. Mahrenholtz and M. Markiewicz, eds.,
WIT Press
,
Southampton, UK
, pp.
59
100
.
25.
CD-adapco
,
2014
, “Star-CCM+ User Guide Version 9.02,” CD-adapco, Melville, NY.
26.
Choi
,
J.
, and
Yoon
,
S. B.
,
2009
, “
Numerical Simulations Using Momentum Source Wave-Maker Applied to RANS Equation Model
,”
Coastal Eng.
,
56
(
10
), pp.
1043
1060
.
27.
Le Méhauté
,
B.
,
1976
,
An Introduction to Hydrodynamics and Water Waves
,
Springer-Verlag
,
New York
, p.
315
.
28.
Dean
,
R.
, and
Dalrymple
,
R.
,
1991
, “
Water Wave Mechanics for Engineers and Scientists
,”
Advanced Series on Ocean Engineering
, Vol.
2
,
World Scientific
, Singapore.
29.
Perić
,
R.
, and
Abdel-Maksoud
,
M.
,
2015
, “
Generation of Free-Surface Waves by Localized Source Terms in the Continuity Equation
,”
Ocean Eng.
,
109
, pp.
567
579
.
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