Geodesic
Predictor-corrector method for numerical solution of Euler and Navier–Stokes equations
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 2, pp. 22-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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A generalization of the schemes of optimal splitting for the numerical solution of the Euler and Navier–Stokes equations in the curvilinear transformed coordinates is performed in this paper. We introduce splitting of the equations, which is uniform in their divergent and non-divergent forms and allows us to construct a class of economic difference schemes. They are realized by scalar sweep methods on the fractional steps and have a large stability margin. The offered algorithm has been tested on stationary and non-stationary problems.
Keywords: Navier–Stokes equations, splitting method, predictor-corrector method, difference scheme.
Mots-clés : Euler equations 
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V. M. Kovenya; A. A. Eremin. Predictor-corrector method for numerical solution of Euler and Navier–Stokes equations. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 2, pp. 22-37. http://geodesic.mathdoc.fr/item/VNGU_2015_15_2_a1/

[1] S. K. Godunov, A. V. Zabrodin, M. Ya. Ivanov, A. N. Kraiko, G. P. Prokopov, Numerical Solution of Multidimensional Problems of Gas Dynamics, Nauka, M., 1976 (in Russian) | MR

[2] A. A. Samarskij, The Theory of Difference Schemes, Marcel Dekker, New York, 2001 | MR | MR

[3] V. M. Kovenya, N. N. Yanenko, Decomposition Method in Problems of Gas Dynamics, Nauka, Novosibirsk, 1981 (in Russian) | MR

[4] Fletcher K., Vychislitelnye metody v dinamike zhidkostei, V 2 t., Mir, M., 1991; C. A. J. Fletcher, Computational Techniques for Fluid Dynamics, v. 1, Fundamental and General Techniques; v. 2, Specific Techniques for Different Flow Categories, Springer, Berlin etc., 1988 | MR | Zbl

[5] O. M. Belotserkovskii, Numerical Modelling in Continuum Mechanics, Nauka, M., 1984 (in Russian) | MR

[6] G. I. Marchuk, Splitting and Alternating Direction Methods, OVM AN SSSR, M., 1986 (in Russian)

[7] V. M. Kovenya, Difference Methods of Solution of Multidimensional Problems, Lecture course, NGU, Novosibirsk, 2004 (in Russian)

[8] Vos J. B., Rizzi A., Darracq D., Hirschel E. H., “Navier–Stokes Solvers in European Aircraft Design”, Progress in Aerospace Sciences, 38:8 (2002), 601–697 | DOI

[9] V. M. Kovenya, Splitting Algorithms as Applied to the Multidimensional Problems of Aerogas Dynamics, Izd. SO RAN, Novosibirsk, 2014 (in Russian)

[10] V. I. Pinchukov, C. Shu, High Order Numerical Methods for Problems of Aerohydrodynamics, Izd. SO RAN, Novosibirsk, 2000 (in Russian)

[11] V. D. Lisejkin, “A survey of methods for constructing structured adaptive grids”, Comput. Math. Math. Phys., 36:1 (1996), 1–32 | MR | Zbl

[12] G. S. Khakimzyanov, Yu. I. Shokin, V. B. Barakhnin, N. Yu. Shokina, Numerical Simulation of Fluid Flows with Surface Waves, Izd. SO RAN, Novosibirsk, 2001 (in Russian)

[13] L. G. Loitsyanskii, Mechanics of Liquids and Gases, Pergamon Press, London, 1966 | MR | MR

[14] V. M. Kovenya, A. Yu. Slyunyaev, “Splitting algorithms as applied to the Navier–Stokes equations”, Comput. Math. Math. Phys., 49:4 (2009), 676–690 | DOI | MR | Zbl

[15] V. I. Zapryagaev, I. N. Kavun, “Experimental study of the reverse flow in the forward separation region in a pulsating flow around a spiked body”, J. Appl. Mech. Tech. Phys., 48:4 (2007), 492–500 | DOI | MR | Zbl