2017
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1
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52
A Numerical Model of Vortex-Induced Vibration on Marine Risers
2
2
The Steger and Warming flux vector splitting implicit scheme is used to numerically solve two dimensional Reynolds Averaged Navier–Stokes (RANS) equations governing the vortex induced vibration of a flexible riser laterally supported by a spring and a damper. The k–ε model is used as turbulence model to simulate the turbulent flow in the wake of the riser. To update the new position of the riser, the lift coefficient obtained from the previous RANS iteration is coupled by the body motion equation. The proposed numerical solution is able to provide fair results in terms of lift coefficient, amplitude of oscillation and the effect of reduced velocity on it. The numerical results are compared with the available experimental and computational data where fairly good agreement even at the lock-in regime has been obtained. Taking wider external boundary, using conservative form of the equations, applying k-ε turbulence model for the separated flow and finally using the variable time step as the lock-in region approaches, are main features of the proposed numerical model.
1
7
hamed
ashuri
hamed
ashuri
hormozgan university
iran
hamedashuri@gmail.com
keyvan
sadeghi
keyvan
sadeghi
Buein Zahra Technical University
iran
keyvan.sadeghi@bzte.ac.ir
saeid
niazi
saeid
niazi
hormozgan university
iran
s.niazi@hotmail.com
vortex-induced vibration
RANS equation
turbulence model
lift coefficient
[1- Griffin, O.M., and Ramberg, S.E., (1982), Some recent studies of vortex shedding with application to marine tubular sand risers. ASME Journal of Energy Resource Technology Vol.104, p.2–13.##2- Bearman, P.W., (1984), Vortex shedding from oscillating bluff bodies. Annual Review of Fluid Mechanics Vol.16, p.195–222.##3- Parkinson, G., (1989), Phenomena and modeling of flow-induced vibrations of bluff bodies. Progression Aerospace Sciences Vol.26, p.169–224.##4- Sarpkaya, T., (2004), A critical review of the intrinsic nature of vortex-induced vibrations, Journal of Fluids and Structures 1Vol.9, p.389–447.##5- Williamson, C.H.K., and Govardhan, R., (2004), Vortex-induced vibrations, Annual Review of Fluid Mechanics, Vol.36, p.413–455.##6- Bearman, P.W., (2000), Developments in Vortex Shedding Research, Workshop on Vortex-Induced Vibrations of Offshore Structures. Sao Paulo, Brazil.##7- Wanderley J.B., and Levi, C., (2005), Vortex induced loads on marine risers, Ocean Engineering Vol.32, p.1281–1295.##8- Khalak, A., and Williamson, C.H.K., (1996) Dynamics of a hydroelastic cylinder with very low mass and damping. Journal of Fluids and Structures, Vol.10, p.455–472.##9- Steger, J.L., and Warming, R.F, (1979), Flux vector splitting of invicid gas dynamic equations with application to finite difference method. NASA. TM-78605.##10- Favre, A., (1965) Equations des gaz turbulents compressibles: 1 Formes Ge´ne´rales. Journal of Mechanics, Vol.4, p.361–390.##11- Jones W.P., and Launder, B.E., (1997), The prediction of relaminarization with a two-equation model of turbulence, International Journal of Heat and Mass Transfer, Vol.15, p.301-314.##12- Goldberg, U.C., (1986), Separated flow treatment with a new turbulence model, AIAA Journal, Vol.24(10), p. 1711-1713.##13- Houzeaux, G., and Codina, R., (2003), A chimera method on a Dirichlet/Neumann (Robin) coupling for the Navier—Stokes equations. Computational Methods Application and Mechanical Engineering, Vol.192, p.3343–3377.##14- Herfjord, K., (1995), A study of two-dimensional separated flow by a combination of the finite element method and Navier–Stokes Equations, Dr. Eng. Theses, The Norwegian Institute of Technology, Trondheim, Norway.##15- Tritton, D.J., (1959), Experiments on the flow past a circular cylinder at low Reynolds number, Journal of Fluid Mechanics, Vol.6, p.## ## ##]
The Effect of Shifting Natural Frequency on the Reduction of Vortex-Induced Vibrations of Marine Risers
2
2
Many procedures suggest for reduction of responses of riser to Vortex Induced Vibrations (VIV). Natural frequencies of marine risers is an important parameter that can affect the responses of riser to VIV. Change of riser properties such as top tension and bending stiffness can alter natural frequencies. In this study effects of riser specifications on the responses and fatigue damage of marine risers were investigated analytically and numerically. For numerically analysis 2D wake-structure coupled model is used for modeling of VIV of riser in two directions of Cross Flow (CF) and In Line (IL). The wake dynamics, including IL and CF vibrations, is represented using a pair of non-linear Van der Pol equations that solved using modified Euler method. The Palmgren–Miner Rule is used for evaluation of fatigue damage. Riser of Amir-Kabir semisubmersible placed in Caspian sea is used for case study. Because VIV is self-limiting, it is showed that lower modes have lower curvature, that in some cases this is lead to lesser stress and also fatigue damage. The results show that for tension dominant modes of vibration, natural frequencies was increased with top tension and for a certain Strouhal frequency, dominant modes of vibration was reduced which leads to reduction of stress and fatigue damage. The results show that stress and fatigue damage increased with module of elasticity of riser and reduction of this leads to reducing of stress and fatigue damage. Therefore suitable procedure for reduction of VIV responses of riser should be selected based on the current velocity.
9
16
Younes
Komachi
Younes
Komachi
Ocean Engineering and Technology Research Center, National Institute for Oceanography
iran
y_komachi@yahoo.com
Said
Mazaheri
Said
Mazaheri
Ocean Engineering and Technology Research Center, National Institute for Oceanography
iran
said.mazaheri@inio.ac.ir
Mohammadreza
Tabeshpour
Mohammadreza
Tabeshpour
School of Mechanical Engineering, Sharif University of Technology
iran
tabeshpour@sharif.edu
VIV
Wake oscillator model
Finite Element Method
Shifting frequency
[Griffin, O.M., and Ramberg, S.E., (1982), Some recent studies of vortex shedding with application to marine tubular sand risers. ASME Journal of Energy Resource Technology Vol.104, p.2–13.##Bearman, P.W., (1984), Vortex shedding from oscillating bluff bodies. Annual Review of Fluid Mechanics Vol.16, p.195–222.##Parkinson, G., (1989), Phenomena and modeling of flow-induced vibrations of bluff bodies. Progression Aerospace Sciences Vol.26, p.169–224.##Sarpkaya, T., (2004), A critical review of the intrinsic nature of vortex-induced vibrations, Journal of Fluids and Structures 1Vol.9, p.389–447.##Williamson, C.H.K., and Govardhan, R., (2004), Vortex-induced vibrations, Annual Review of Fluid Mechanics, Vol.36, p.413–455.##Bearman, P.W., (2000), Developments in Vortex Shedding Research, Workshop on Vortex-Induced Vibrations of Offshore Structures. Sao Paulo, Brazil.##Wanderley J.B., and Levi, C., (2005), Vortex induced loads on marine risers, Ocean Engineering Vol.32, p.1281–1295.##Khalak, A., and Williamson, C.H.K., (1996) Dynamics of a hydroelastic cylinder with very low mass and damping. Journal of Fluids and Structures, Vol.10, p.455–472.##Steger, J.L., and Warming, R.F, (1979), Flux vector splitting of invicid gas dynamic equations with application to finite difference method. NASA. TM-78605.##Favre, A., (1965) Equations des gaz turbulents compressibles: 1 Formes Ge´ne´rales. Journal of Mechanics, Vol.4, p.361–390.##Jones W.P., and Launder, B.E., (1997), The prediction of relaminarization with a two-equation model of turbulence, International Journal of Heat and Mass Transfer, Vol.15, p.301-314.##Goldberg, U.C., (1986), Separated flow treatment with a new turbulence model, AIAA Journal, Vol.24(10), p. 1711-1713.##Houzeaux, G., and Codina, R., (2003), A chimera method on a Dirichlet/Neumann (Robin) coupling for the Navier—Stokes equations. Computational Methods Application and Mechanical Engineering, Vol.192, p.3343–3377.##Herfjord, K., (1995), A study of two-dimensional separated flow by a combination of the finite element method and Navier–Stokes Equations, Dr. Eng. Theses, The Norwegian Institute of Technology, Trondheim, Norway.##Tritton, D.J., (1959), Experiments on the flow past a circular cylinder at low Reynolds number, Journal of Fluid Mechanics, Vol.6, p.## ##]
Drilling Risk Identification, Filtering, Ranking and Management
2
2
Drilling Operations are exposed to a variety of hazards, some of which may be location and activity dependent and each could pose different risk from different paths. Drilling operation may be vulnerable to hurricanes in one region and be exposed to Geohazards in another. However, there are other hazards, (e.g. corrosion, age degradation, poor maintenance), which equally affects every rig. Identifying what can go wrong and their likelihood and possible consequences provides insight into vulnerability of the operation and helps to generate mitigation options. Filtering and Ranking risk contributors enable to decide priorities and to focus on the most important risk contributors. This paper offers a framework to identify, assess, prioritize, and manage drilling risks, which includes: (1) a holistic approach to risk identification; (2) prioritization of a large number of risk influencing factors or risk scenarios; (3) structured elicitation of experts’ opinion and effective integration of experts judgment into qualitative and quantitative analyses to supplement limited data availability; (4) extreme and catastrophic event analysis; and (5) use of multi-objective framework to evaluate risk management priorities.
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26
Sirous
Yasseri
Sirous
Yasseri
Brunel University
United kingdom
sirous.yasseri@gmail.com
Drilling Risk assessment
Risk influencing factors
Risk filtering &
Ranking
Analytic Hierarchical Process
[1- Kaplan, S. and B.J. Garrick, B.J., On the Quantitative Definition of risk, 1981, Risk Analysis Vol. l (1), pp11-27, 1981.##2- Kaplan, S., Haimes, Y.Y. and Garrick, B.J., Fitting hierarchical holographic modelling (HHM) into the theory of scenario structuring and a refinement to the quantitative definition of risk, Risk Analysis, Vol.21 (5): pp 807-819, 2001.##3- Leveson N., Applying systems thinking to analyse and learn from events, Safety Science, Vol.49, pp 55–64, 2011.##4- Ouchi, F., A Literature Review on the Use of Expert Opinion in Probabilistic Risk Analysis, World Bank Policy Research Working Paper 3201, February 2004, last accessed 23/03/2015. http://wwwwds.worldbank.org/external/default/WDSContentServer/WDSP/IB/2004/04/15/000009486_20040415130301/additional/115515322_20041117173031.pdf##5- Pitblado, R. and Nelson, W. R., Advanced Safety Barrier Management with Inclusion of Human and Organizational Aspects, Chemical engineering transactions Vol. 31, 2013. http://www.aidic.it/cet/13/31/056.pdf##6- Ramanathan, R. and Ganesh, L. S., Group preference aggregation methods employed in the AHP: an evaluation and an intrinsic process for deriving members, European Journal of Operational Research 79, 249–265, 1994. ##7- Ramanathan, R., A note on the use of the analytic hierarchy process for environmental impact assessment R. Journal of Environmental Management Vol.63, pp 27–35, 2001.##8- Saaty, T.L., The analytic hierarchy process, New York- McGraw Hill 1980.##9- Saaty, T., How to make a decision: the analytic hierarchy process, European journal of operational Research, Vol. 48(1): 9-26, 1990. ##10- Yasseri, S., Subsea technologies selection using analytic hierarchy process, International journal of underwater technology, Society for Underwater Technology, Volume 30, Number 3, pp. 151-164, 2012. ## ##]
Subsea Corrosion Management: Challenges and Limitations
2
2
Subsea structures such as manifolds, line pipes and flow lines are important investments. Also because of the sensitivity of environmental issues, corrosion of these structures is of vital importance. Subsea corrosion management is different from on-shore and shallow water off-shore corrosion management in mainly three factors: materials, corrosion management practice and cathodic protection. There are important limitations in many aspects of these three factors that make them different from their “counterparts” in other industries. In this paper, some of these differences especially with regards to corrosion prediction softwares and associated design strategies are addressed and discussed.
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32
Reza
Javaherdashti
Reza
Javaherdashti
Parscorrosion Consultants
Australia
javaherdashti@yahoo.com
Subsea structures Integrity-Corrosion prediction models-CRA-Cathodic protection
[1. Guide for building and classing subsea pipeline systems-Chapter 2, Section1, American Bureau of Shipping (ABS), Houston, TX, USA, May 2006 (updated March 2008).##2. S. Missori, F. Murdolo, A. Sili, “Microstructural Characterisation of a stainless steel-cladded carbon steel”, Metallurgical Science and Technology, Vol.19.No.2, December 2001, p.21-24.##3. V. Olden “FE modeling of hydrogen induced stress cracking in 25% Cr duplex stainless steel”, PhD Thesis, Norwegian University of Science and Technology, Trondheim, August 2008. ##4. “Design guideline to avoid hydrogen induced stress cracking in subsea duplex stainless steel”, NORSOK Workshop Agreement-HISC Guideline for duplex stainless steel-M-WA-01, Rev.1, October 2005##5. H.H. Uhlig, Corrosion and corrosion control. 2nd edn. John Wiley & Sons, West##Sussex, England, 1971.##6. J. Marsh and T. Teh “Conflicting Views: CO2 Corrosion Models, Corrosion Inhibitor Availability Philosophies, and the Effect on Subsea Systems and Pipeline Design”, SPE 109209, Offshore Europe 2007, Aberdeen, Scotland, U.K., 4–7 September 2007.##7. C. de Waard, U. Lotz, D.E. Milliams, “Predictive model for CO2 corrosion engineering in wet natural gas pipelines”, Corrosion, Vol.47, No.12, December 1991, pp.976-985.##8. C. de Waard, U. Lotz “Prediction of CO2 corrosion of car bon steel”, NACE CORROSION’93, Paper 69, March 1993, New Orleans, 1993, USA.##9. A. Petersen, R. Chapman, B. Hedges “Corrosion prediction with Cassnadra”, S/UTG/013/03, bp Upstream Technology Group Sunbury, 01/03/03.##10. R. Johnsen, “Corrosion of carbon steel in hydrocarbon environments”, Norwegian University of Science and Technology, 20/09/2005.##11. R. Javaherdashti, “Microbiologically influenced corrosion-An engineering insight”, Springer, 2008, UK.##12. R. Javaherdashti, "MIC myths: Avoiding common pitfalls in the practice of hydrotesting and likelihood of Microbial induced corrosion", Corrosion Management, January-February 2009.##13. X. Wang, J. Duan, Y. Li, J. Zhang, S. Ma, B. Hou “Corrosion of steel structures in sea-bed sediments”, Bulletin of Materials Science, Vol.28, No.2, pp.81-85, April 2005.##14. Offshore Standard DNV- OS-F101, Section 5, B 507, Det Norske Veritas, Norway, January 2000.##15. S. Eliassen “New concept for cathodic protection of offshore pipelines to reduce hydrogen induced stress cracking (HISC) in high strength 13% Cr stainless steel”, Corrosion Engineering, Science, and Technology, Vol.39, No.1, pp.31-37, 2004.## ##]
A 3D Numerical Study of Cyclone Gonu Waves Impact on Ramin Port
2
2
In this paper the TELEMAC-3D model has been hired to simulate and study the high waves’ interaction with coastal structures. Therefore a special arrangement of TELEMAC-3D has been prepared in this study to simulate wave generation, coastal processes, wave set-up and overtopping over coastal structures. Experimental data has been used to verify this arrangement of the model. Thereafter, the model has used to simulate the interaction of waves induced by Cyclone Gonu and Ramin port breakwaters. Quality comparison between images provided by Iran Fisheries Organization during the Gonu event and the TELEMAC3D results concludes that the numerical model could simulate the incidence with a good accuracy. Different kind of results like inundation area, wave overtopping discharge over the breakwaters and wave penetration in port were obtained in this simulation.
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41
Fatemeh
Hajivalie
Fatemeh
Hajivalie
Iranian National Institute for Oceanography and Atmospheric Science
iran
hajivalie@inio.ac.ir
Ahmad
Arabzadeh
Ahmad
Arabzadeh
Iranian National Institute for Oceanography and Atmospheric Science
iran
ahmadarabzadeh@inio.ac.ir
TELEMAC-3D
Wave overtopping
Wave diffraction
Wave penetration
Inundation
[Dibajnia, M., Soltanpour, M., Nairn, R., Allahyar, M., 2010, In: Charabi, Y. (Ed.), Indian Ocean Tropical Cyclones and Climate Change. Springer. 373 pp.##Fritz, H.M., Blount, C.D., Albusaidi, F.B., Al-Harthy, A.H.M., 2010, Cyclone Gonu storm surge in Oman. Estuarine, Coastal and Shelf Science 86, 102–106.##Golshani, A., Taebi, S., 2008, Numerical modeling and warning procedures for Gonu Super Cyclone along Iranian Coastlines. In: Wallendorf, L., et al. (Ed.), Proceedings of the Third COPRI Solutions to Coastal Disasters Conference. ASCE, Oahu, HI. 13–16 April 2008.##Hsiao, S.C., Lin, T.C., 2010, Tsunami like solitary waves impinging and overtopping an impermeable seawall: Experimental and RANS modeling. Coastal Engineering. 57.1-18.##Khalilabadi, M. R. and Mansouri, D., 2013, The effect of super cyclone “GONU” on sea level variation along Iranian coastlines, Khalilabadi, M. R. and Mansouri, D., 2013, The effect of super cyclone “GONU” on sea level variation along Iranian coastlines, Indian Journal of Geo-Marine Science, Vol. 42(4), pp 470-475.##Mashhadi, L., Hajizadeh-Zaker, N., Soltanpour, M. Moghimi, S., 2013, Numerical simulation of waves and storm surge induced by the Gonu Tropical Cyclone in the Chahbahar bay area. Journal of Marine Engineering, 17, 37-50, (in Persian). ##Pham, C., Goeury, C., and Joly, A., 2016, TELEMAC modeling syste, TELEMAC-3D software operating manual (Rep. No. Release 7.0).##Shah-hosseini, M., Morhange, C., Naderi Beni, A., Marriner, N., Lahijani, H., Hamzeh, M., Sabatier, F., 2011, Coastal boulders as evidence for high-energy waves on the Iranian coast of Makran, Marine Geology, Volume 290, Issues 1–4, Pages 17-28.## ##]
SPH Simulation of Waves Associated with Underwater Explosion
2
2
The current manuscript presents the validation of Smoothed Particle Hydrodynamics (SPH) techniques for wave generation by underwater explosion, utilizing the so-called DualSPHysics numerical model. This numerical method is used to analyze generated waves which are initiated by man-made or natural explosions below free surface level of sea. In spite of the modeling limitations (e.g. absence of open boundary conditions), reasonable agreement is accomplished with predictions of the existing formula as well as experimental results. This proved that SPH techniques such as incorporated in DualSPHysics are becoming a suitable alternative to existing classical approaches to this particular water waves problem. It is also provided an inherently more accurate computational for the prediction of wave characteristics generated by underwater explosions.
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52
Omid Reza
Safiyari
Omid Reza
Safiyari
Iranian National Institute for Oceanography and Atmospheric Science (INIOAS)
iran
o.r.safiyari@inio.ac.ir
Mahmood Reza
Akbarpour Jannat
Mahmood Reza
Akbarpour Jannat
Iranian National Institute for Oceanography and Atmospheric Science (INIOAS)
iran
akbarpour@inio.ac.ir
Babak
Banijamali
Babak
Banijamali
Darya Bandar Engineering Consultant Company (DBC)
iran
banijamali.babak@gmail.com
Underwater Explosion
Smoothed Particle Hydrodynamics
Graphical Processing Unit
Numerical Modeling
Explosion Generated Water Waves
[Altomare C, Crespo AJC, Rogers BD, Dominguez JM, Gironella X, Gomez-Gesteira M (2014) “Numerical modelling of armour block sea breakwater with smoothed particle hydrodynamics”, Computers & Structures Vol. 130, pp 34-45.##Altomare C, Crespo AJC, Dominguez JM, Gomez-Gesteira M, Suzuki T, Verwaest T (2015) “Applicability of Smoothed Particle Hydrodynamics for estimation of sea wave impact on coastal structures”, Coastal Engineering Journal Vol. 96, pp 1-12.##Barreiro A, Crespo AJC, Domínguez JM, Gómez-Gesteira M (2013) “Smoothed Particle Hydrodynamics for coastal engineering problems” Computers & Structures Vol. 120, pp 96-106.##Bottin RR (1990) “Impulsive waves generated by falling weights in shallow water”, Final Technical Report CERC-90-9. Coastal Engineering Research Center, DEPARTMENT OF THE ARMY, Waterways Experiment Station, Corps of Engineers, 3909 Halls Ferry Road, Vicksburg, Mississippi 39180-6199. ##Bryant AR (1950) “Surface waves produced by underwater explosions Comparison of the theory of W.G. Penney with experimental results for a 32-lb. charge”, Underwater Explosion Research, Vol. II, ONR, Dept. of Navy, pp 701-706.##Crespo AJC, Altomare C, Dominguez JM, Suzuki T, Verwaest T, Gomez-Gesteira M (2015) “SPH modeling in coastal engineering”, E-proceedings of the 36th IAHR World Congress. The Hague, the Netherlands.##Crespo AJC, Domínguez JM, Gómez-Gesteira M, Barreiro A, Rogers BD, Longshaw S, Canelas R, Vacondio R (2013) “User Guide for DualSPHysics v3.0”.##Domínguez JM, Crespo AJC, Gómez-Gesteira M, Marongiu JC (2011) “Neighbour lists in Smoothed Particle Hydrodynamics”, International Journal for Numerical Methods in Fluids, Vol. 67, Issue 12, pp 2026-2042, doi:10.1002/fld.2481.##Domínguez JM, Crespo AJC and Gómez-Gesteira M (2013) “Optimization strategies for CPU and GPU implementations of a smoothed particle hydrodynamics method”, Computer Physics Communications, Vol. 184, Issue 3, pp 617-627, doi:10.1016/j.cpc.2012.10.015.##Falade A and Holt M (1978) “Surface waves generated by shallow underwater explosions”, Physics of Fluids (1958-1988), AIP Publishing, Physics of Fluids, Vol. 21, Issue 10, p. 1709.##Fuchs RA (1952) “Theory of surface waves produced by underwater explosions” Technical Report Series No. 3, Issue No. 335, 9 PP. University of California, Institute of Engineering Research, Berkeley, California.##Gomez-Gesteira M, Rogers BD, Crespo AJC, Dalrymple RA, Narayanaswamy M, Dominguez JM (2012) “SPHysics - development of a free-surface fluid solver – Part 1: Theory and formulations”, Computers & Geosciences Vol. 48, pp 289-299. ##Gomez-Gesteira M, Rogers BD, Crespo AJC, Dalrymple RA, Narayanaswamy M, Dominguez JM (2012) “SPHysics - development of a free-surface fluid solver – Part 2: Efficiency and test cases”, Computers & Geosciences Vol. 48, pp 300-307.##Kirkwood JG and Seeger RJ (1950) “Surface waves from an underwater explosion”, Underwater Explosion Research, Vol. II, ONR, Dept. of Navy, pp 707-760.##Kolsky H, Lewis JP, Sampson MT, Shearman AC, Snow CI (1949) “Splashes from Underwater Explosions”, Proceeding of Royal Society of London, Vol. 196, pp. 379-402.##Kozachenko LS and Khristoforov BD (1972) “Surface events during underwater explosions”, Translated from Fizika Goreniya i Vzryva, Vol. 8, No. 3, pp. 433-438.##Kranzer HC and Keller JB (1955) “Water waves produced by explosion”, New York University, Institute of Mathematical Sciences, IMM-NYU 222, 26 pp.##Kranzer HC and Keller JB (1959) “Water Waves Produced by Explosions”, AIP Publishing, Journal of Applied Physics, Vol., Issue 3, p. 398.##LeMehaute B and Wang S (1996) “Water waves generated by underwater explosion”, World Scientific, River Edge.##Liu MB, Liu GR, Lam KY, Zong Z (2003) “Smoothed particle hydrodynamics for numerical simulation of underwater explosion”, Computational Mechanics Vol.30, pp 106-118.##Mader CL (1976) “Calculations of waves formed from surface cavities”, Proc. of 15th Conf. on Coastal Engineering 15:1079-1092. doi: 10.9753/icce.v15.%25p, ISSN: 2156-1028.##Monaghan JJ and Gingold RA (1983) “Shock simulation by the particle method SPH”, J. of comp. Phys. Vol. 52, pp 374-389, doi: 10.1016/0021-9991(83)90036-0.##Noda EK (1971) “Water waves generated by a local surface disturbance”, J of Geophysical Research 76:7389-7400. doi: 10.1029/JC076i030p07389.##Penney WG (1950) “Gravity waves produced by surface and underwater explosions”, Underwater Explosion Research, Vol. II-The gas globe, Office of Naval Research, Department of the Navy, pp 679-700.##Prins JE (1957) “Water waves due to a local disturbance”, Proc. of 6th Conf. on Coastal Engineering 6:147-162. doi: 10.9753/icce.v6.8.##Swegle JW and Attaway SW (1995) “On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations”, Comp. Mech. Vol. 17, pp 151-168.##Whalin RW (1965) “Water waves produced by underwater explosions: propagation theory for regions near the explosion”, Journal of Geophysical Research, Vol.70, No. 22, pp. 5541-5549.##www.SPHysics.org, Official site of SPHysics software.##www.dual.SPHysics.org, Official site of DualSPHysics software.##www.DTIC.mil, Official site of Defense Technical Information Center.## ##]