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“Efficient numerical simulation of ocean hydrodynamics by a splitting procedure”

Authors: Hans Berntsen, Zygmunt Kowalik, Steinar Sælid and Karstein Sørli,
Affiliation: SINTEF, Institute of Meteorology and Water Management, Poland and NTNU, Department of Engineering Cybernetics
Reference: 1981, Vol 2, No 4, pp. 181-199.

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Keywords: Physical oceanography, numerical modeling, fast and slow modes, splitting, efficiency, accuracy, stability

Abstract: A splitting algorithm for fast and slow modes of ocean hydrodynamics is presented. The purpose of the splitting is to reduce the large amount of computational work needed for simulating long real-time periods. The essential point of the splitting is that the external gravity wave terms are extracted from the fully three-dimensional equations of horizontal motion, allowing the reduced equations to be integrated with a larger time step than the original model. The fast external gravity waves are traced by a depth integrated system which is weakly coupled to the reduced three-dimensional momentum equations. The split model shows a radical decrease in computational time and the accuracy is of the same order as in the non-split case.

PDF PDF (1633 Kb)        DOI: 10.4173/mic.1981.4.1

DOI forward links to this article:
  [1] Jarle Berntsen (2002), doi:10.1175/1520-0426(2002)019<1403:IPEISC>2.0.CO;2
  [2] Øyvind Thiem, Magda Carr, Jarle Berntsen and Peter A. Davies (2011), doi:10.1007/s10236-011-0396-5
  [3] Jarle Berntsen and Øyvind Thiem (2007), doi:10.1007/s10236-007-0118-1
  [4] Yngve Heggelund, Frode Vikebø, Jarle Berntsen and Gunnar Furnes (2004), doi:10.1016/j.csr.2004.07.005
  [5] Jarle Berntsen, Jiuxing Xing and Alan M. Davies (2009), doi:10.1007/s10236-009-0227-0
  [6] Knut S. Seim, Ilker Fer and Helge Avlesen (2012), doi:10.1016/j.csr.2011.11.016
  [7] S. Holte (1982), doi:10.1016/0278-4343(82)90023-1
  [8] Alfatih Ali, Øyvind Thiem and Jarle Berntsen (2013), doi:10.1007/s10236-013-0638-9
  [9] Meng Yu Lin and Liang Hsiung Huang (2008), doi:10.1080/02533839.2008.9671363
  [10] Mark Reed and Jens G. Balchen (1982), doi:10.4173/mic.1982.2.1
  [11] Alexander F. Shchepetkin and James C. McWilliams (2011), doi:10.1016/j.ocemod.2011.01.010
  [12] Øyvind Thiem and Jarle Berntsen (2006), doi:10.1016/j.ocemod.2005.05.001
  [13] Jens G. Balchen (2000), doi:10.4173/mic.2000.1.1
  [14] Jarle Berntsen, Jiuxing Xing and Alan M. Davies (2008), doi:10.1016/j.csr.2008.03.029
  [15] Øyvind Thiem and Jarle Berntsen (2009), doi:10.1007/s10236-009-0220-7
  [16] Jarle Berntsen, Jiuxing Xing and Guttorm Alendal (2006), doi:10.1016/j.csr.2006.02.014
  [17] Alfatih Ali, Øyvind Thiem and Jarle Berntsen (2011), doi:10.1007/s10236-011-0393-8
  [18] Knut S. Seim, Ilker Fer and Jarle Berntsen (2010), doi:10.1016/j.ocemod.2010.06.002
  [19] Dag Slagstad, Kjell Støle-Hansen and Harald Loeng (1990), doi:10.4173/mic.1990.4.1
  [20] Alexander F. Shchepetkin and James C. McWilliams (2009), doi:10.1016/S1570-8659(08)01202-0
  [21] Jarle Berntsen (2011), doi:10.1016/j.ocemod.2011.02.006
  [22] KJELL STØLE-HANSEN and DAG SLAGSTAD (1991), doi:10.1111/j.1751-8369.1991.tb00632.x
  [23] Jarle Berntsen and Gunnar Furnes (2005), doi:10.1016/j.csr.2004.09.025
  [24] Arild Sundfjord, Ingrid Ellingsen, Dag Slagstad and Harald Svendsen (2008), doi:10.1016/j.dsr2.2008.05.027
  [25] Øyvind Thiem, Elisa Ravagnan, Jan Helge Fosså and Jarle Berntsen (2006), doi:10.1016/j.jmarsys.2005.12.004
  [26] Eirik Keilegavlen and Jarle Berntsen (2009), doi:10.1016/j.ocemod.2009.02.006
  [27] Øyvind Thiem, Jarle Berntsen and Bjørn Gjevik (2006), doi:10.1016/j.csr.2006.02.016
  [28] Jon Bergh and Jarle Berntsen (2010), doi:10.1007/s10236-009-0242-1
  [29] Birgit Kjoss Lynge, Jarle Berntsen and Bjørn Gjevik (2010), doi:10.1007/s10236-010-0309-z

[1] BALCHEN, J.G. (1979). Mathematical and numerical modeling of physical and biological processes in the Barents Sea, Statistical Ecology Series, Ed. G. P. Patil.Burtonville, Maryland, U.S.A.: International Cooperative Publishing House.
[2] GOURLAY, A.R. (1977). Splitting methods for time dependent partial differential equations, The State of the Art in Numerical Analysis, ed. by D. Jacobs.Academic Press, pp. 757-796.
[3] LEENDERTSE, J.J., ALEXANDER, R. C., LIU, S. K. (1973). A three-dimensional model for estuaries and coastal areas, Vol. I, Principles of computation, R-1417-OWRR.The Rand Corporation, Santa Monica.
[4] LEENDERTSE, J.J., LIU, S. K. (1975). A three-dimensional model for estuaries and coastal areas, Vol. II, Aspects of computation, R-1764-OWRT.The Rand Corporation, Santa Monica.
[5] LIU, S.K., LEENDERTSE, J.J. (1978). Multidimensional numerical modeling of estuaries and coastal seas, Advances in Hydroscience, Vol. 11.Academic Press, pp. 95-164.
[6] MADALA, R.V., PIACSEK, S.A. (1977). A semi-implicit numerical model for baroclinic oceans, J. Comp. Physics, 23, pp. 167-178 doi:10.1016/0021-9991(77)90119-X
[7] MARCHUK, G.I. (1975). Methods of numerical mathematics, New York: Springer-Verlag.
[8] MUNCH, W.H., ANDERSEN, E.R. (1948). Note on the theory of thermocline, J. Mar. Research, 7, 276-295.
[9] PEACEMAN, D.W., RACHFORD, H.H., Jr. (1955). The numerical solution of parabolic and elliptic differential equations, SIAM J., 3, pp. 28-41.
[10] PHILLIPS, O.M. (1966). The dynamics of upper layer, University Press.

  title={{Efficient numerical simulation of ocean hydrodynamics by a splitting procedure}},
  author={Berntsen, Hans and Kowalik, Zygmunt and Sælid, Steinar and Sørli, Karstein},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


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