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Sukhov, V. B.

Splitting schemes for the Ocean dynamics equations. (English. Russian original) Zbl 1304.86002

Mosc. Univ. Math. Bull. 64, No. 1, 29-33 (2009); translation from Vest. Mosk. Univ. Mat. Mekh. 64, No. 1, 28-33 (2009).
Summary: A splitting scheme in physical processes is proposed for a system of large-scale ocean dynamics equations. The convergence to an exact solution is proved for this scheme.

MSC:

86A05 Hydrology, hydrography, oceanography
86-08 Computational methods for problems pertaining to geophysics
35Q35 PDEs in connection with fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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\textit{V. B. Sukhov}, Mosc. Univ. Math. Bull. 64, No. 1, 29--33 (2009; Zbl 1304.86002); translation from Vest. Mosk. Univ. Mat. Mekh. 64, No. 1, 28--33 (2009)
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References:

[1] G. I. Marchuk, Splitting Methods (Nauka, Moscow, 1988) [in Russian].
[2] A. A. Samarskii and P. N. Vabishchevich, Additive Schemes for Problems of Mathematical Physics (Nauka, Moscow, 2001) [in Russian]. · Zbl 1094.65082
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[4] R. Rannacher, ”On Chorin’s Projection Method for the Incompressible Navier-Stokes Equations,” in Navier-Stokes Equations II – Theory and Numerical Methods, Lect. Notes Math. Vol. 1530 (Springer, Berlin, 1992), pp. 167–183. · Zbl 0769.76053
[5] G. I. Marchuk and A. S. Sarkisyan, Mathematical Modeling of the Ocean Circulation (Nauka, Moscow, 1988) [in Russian]. · Zbl 0712.76006
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[7] R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis (North-Holland, Amsterdam, New York, Oxford, 1979; Mir, Moscow, 1981).
[8] G. Kobelkov, ”Existence of a Solution ”in the Large” for the 3D Large-Scale Ocean Dynamics Equations,” C. r. Acad. sci. Paris. Ser. 1. 343. 283 (2006). · Zbl 1102.35003
[9] M. A. Olshanskii, ”On the Stokes Problem with Model Boundary Conditions,” Matem. Sborn. 188(4), 127 (1997) [Sbornik: Math. 188 (4), 603 (1997)].
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