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Resolution by Galerkin method with a special basis of a geophysical flow in open sea: A Calvi’s bay simulation. (English) Zbl 0969.76067

Summary: We present numerical solution of a geophysical flow by Galerkin method. First, we expose briefly a three-dimensional model and derive a shallow water model. Then we give some theoretical results in order to justify the numerical approach presented. Lastly, we describe different steps of the solution as well as numerical tools. We apply this method to simulate the Calvi’s bay flow, and compare results on the depth-average velocity obtained by the shallow-water model and by a three-dimensional model.

MSC:

76M22 Spectral methods applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography
86-08 Computational methods for problems pertaining to geophysics
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[1] J.C.J. Nihoul, Modèles mathématiques et Dynamique de l’environnement, Elsevier, Amsterdam, 1977; J.C.J. Nihoul, Modèles mathématiques et Dynamique de l’environnement, Elsevier, Amsterdam, 1977
[2] J.C.J. Nihoul, Modelling of Marine Systems, Elsevier Oceanography Series, Elsevier, Amsterdam, 1975; J.C.J. Nihoul, Modelling of Marine Systems, Elsevier Oceanography Series, Elsevier, Amsterdam, 1975
[3] OPA, Version 8, Ocean General Circulation Model, Reference Manual, April 1997; OPA, Version 8, Ocean General Circulation Model, Reference Manual, April 1997
[4] P. Marchesiello, Simulation de la circulation océanique dans l’atlantique sud avec un modéle numérique à coordonnée sigma, Ph.D. Thesis, Université Joseph Fourier, Grenoble 1 Grenoble, 1995; P. Marchesiello, Simulation de la circulation océanique dans l’atlantique sud avec un modéle numérique à coordonnée sigma, Ph.D. Thesis, Université Joseph Fourier, Grenoble 1 Grenoble, 1995
[5] Davies, A. M., Numerical problems in simulating tidal flows with a frictional-velocity-dependent eddy viscosity ant the influence of stratification, Int. J. Numer. Meth. Fluid, 16, 105-131 (1993) · Zbl 0825.76551
[6] Davies, A. M.; Owen, A., Three-dimensional numerical sea model using the Galerkin method with a polynomial basis set, Appl. Math. Modelling, 3, 421-428 (1979) · Zbl 0437.76014
[7] B. diMartino, F.J. Chatelon, P. Orenga, The nonlinear Galerkin method applied to shallow water equations M3AS, to appear; B. diMartino, F.J. Chatelon, P. Orenga, The nonlinear Galerkin method applied to shallow water equations M3AS, to appear
[8] Orenga, P., Un théorème d’existence de solutions d’un problème de shallow water, Arch. Rational Mach. Anal., 130, 183-204 (1995) · Zbl 0839.76007
[9] F.J. Chatelon, P. Orenga, On a non-homogeneous shallow-water problem, \(M^2\); F.J. Chatelon, P. Orenga, On a non-homogeneous shallow-water problem, \(M^2\) · Zbl 0871.76009
[10] J.C.J. Nihoul, A three-dimensional marine circulation model in a remote sensing perspectives, Annales Géophysicae 2 (1984) 433-442; J.C.J. Nihoul, A three-dimensional marine circulation model in a remote sensing perspectives, Annales Géophysicae 2 (1984) 433-442
[11] P. Orenga, F.J. Chatelon, C. Fluixa, Analysis of some oceanography physics problems by the Galerkin’s method, in: The mathematics of models for climatology and environment, NATO Advanced Study, 1995; P. Orenga, F.J. Chatelon, C. Fluixa, Analysis of some oceanography physics problems by the Galerkin’s method, in: The mathematics of models for climatology and environment, NATO Advanced Study, 1995 · Zbl 0891.76067
[12] A.E. Gill, Atmosphere, Ocean Dynamics, International Geophysics Series, vol. 30, Academic press, New York, 1982; A.E. Gill, Atmosphere, Ocean Dynamics, International Geophysics Series, vol. 30, Academic press, New York, 1982
[13] Pedlosky, J., Ocean Circulation Theory (1996), Springer: Springer Berlin · Zbl 0159.59402
[14] P. Orenga, Analyse de quelques problèmes d’océanographie physique, Université de Corse Corte, 1992; P. Orenga, Analyse de quelques problèmes d’océanographie physique, Université de Corse Corte, 1992
[15] C. Fluixa, Analyse d’un problème d’océanographie physique en dimension trois par la méthode de Galerkin, Ph.D. Thesis, Université de Corse Corte avr, 1997; C. Fluixa, Analyse d’un problème d’océanographie physique en dimension trois par la méthode de Galerkin, Ph.D. Thesis, Université de Corse Corte avr, 1997
[16] B. di Martino, P. Orenga, Resolution to a three-dimensional physical oceanographic problem using the nonlinear Galerkin method, Int. J. Numer. Meth. Fluid, to appear; B. di Martino, P. Orenga, Resolution to a three-dimensional physical oceanographic problem using the nonlinear Galerkin method, Int. J. Numer. Meth. Fluid, to appear · Zbl 0949.76067
[17] Davies, A. M., A three-dimensional model of the northwest european continental shelf with application to the \(M_4\) tide, J. Physical Oceanography, 16, 797-813 (1986)
[18] J.C.J. Nihoul, Hydrodynamic models of shallow continental seas, Application to the North Sea, Etienne Riga, 1982; J.C.J. Nihoul, Hydrodynamic models of shallow continental seas, Application to the North Sea, Etienne Riga, 1982
[19] Orenga, P., Construction d’une base spéciale pour la résolution de quelques problèmes d’Océanographie physique en dimension deux, CRAS, 314, 587-590 (1992) · Zbl 0747.76047
[20] C. Giacomoni, B. di Martino, P. Orenga, Analysis of some shallow water problems with rigid-lid hypothesis, 1999, preprint; C. Giacomoni, B. di Martino, P. Orenga, Analysis of some shallow water problems with rigid-lid hypothesis, 1999, preprint · Zbl 1178.76090
[21] A. Norro, Étude pluridiciplinaire d’un milieu côtié. Approches expérimentales de la modélization de la baie de Calvi (Corse), Ph.D. Thesis, Université de Liège, 1995; A. Norro, Étude pluridiciplinaire d’un milieu côtié. Approches expérimentales de la modélization de la baie de Calvi (Corse), Ph.D. Thesis, Université de Liège, 1995
[22] Marion, M.; Temam, R., Nonlinear Galerkin methods, SIAM J. Numer. Anal., 26, 5, 1139-1157 (1989) · Zbl 0683.65083
[23] A.M. Davies, Solution of the 3D linear hydrodynamic equations using an enhanced eigenfunction approach, Int. J. Numer. Meth. Fluid 13 (1991) 235-250; A.M. Davies, Solution of the 3D linear hydrodynamic equations using an enhanced eigenfunction approach, Int. J. Numer. Meth. Fluid 13 (1991) 235-250 · Zbl 0724.76064
[24] J.C.J. Nihoul, Lecture on Turbulence, ELE, Liège, 1979; J.C.J. Nihoul, Lecture on Turbulence, ELE, Liège, 1979
[25] J.C.J. Nihoul, E. Deleersnijder, S. Djenidi, Modelling the general circulation of shelf seas bye 3D k-\(ε\); J.C.J. Nihoul, E. Deleersnijder, S. Djenidi, Modelling the general circulation of shelf seas bye 3D k-\(ε\)
[26] F. Bosseur and P. Orenga. Détermination de conditions aux limites en mer ouverte avec une méthode de contrôle optimal Nonlinear Partial Differential Equations and their applications, accepted; F. Bosseur and P. Orenga. Détermination de conditions aux limites en mer ouverte avec une méthode de contrôle optimal Nonlinear Partial Differential Equations and their applications, accepted · Zbl 1011.35133
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