Geodesic
Accuracy of the numerical solution of the equations of diffusion-convection using the difference schemes of second and fourth order approximation error
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 1, pp. 47-62 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper deals with the scheme of the second and fourth order approximation error for solving convection-diffusion problems. To model initial boundary value problem in the case when the functions of the right and the initial condition can be represented by finite sums of Fourier series in the trigonometric basis, we investigated the accuracy of difference schemes. It was found that the accuracy of the numerical solution depends on the number of units attributable to half the wavelength corresponding to the most high frequency harmonics in the final sum of the Fourier series, necessary to describe the behavior of calculated objects. The dependence of the diffusion approximation error terms difference schemes of second and fourth order of accuracy of the number of nodes. The comparison of the calculation results of two-dimensional convection-diffusion problems and tasks of the Poisson-based schemes of the second and fourth order accuracy. In the expediency of transition to a scheme of high accuracy for solving applied problems of the estimates and is easy to obtain the numerical values of the gain in computation time by using schemes of higher order accuracy.
Keywords: accuracy difference schemes, approximation error.
Mots-clés : convection-diffusion equation 
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A. I. Sukhinov; A. E. Chistakov; M. V. Iakobovskii. Accuracy of the numerical solution of the equations of diffusion-convection using the difference schemes of second and fourth order approximation error. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 1, pp. 47-62. http://geodesic.mathdoc.fr/item/VYURV_2016_5_1_a4/

[1] A.I. Sukhinov, A.E. Chistyakov, A.A. Semenyakina, A.V. Nikitina, “Parallel Implementation of the Tasks of Transport Agents and the Bottom Surface of the Restoration on the Basis of Schemes of Increased Order of Accuracy”, Computational Methods and Programming, 16:2 (2015), 256–267

[2] A.E. Chistyakov, A.A. Semenyakina, “Use of Interpolation Methods for Recovery Bottom Surface”, Izvestiya SFedU. Engineering Sciences, 2013, no. 4, 21–28

[3] A.I. Sukhinov, A.E. Chistyakov, “Parallel Implementation of a Threedimensional Hydrodynamic Model of Shallow Water Basins on Supercomputing Systems”, Computational Methods and Programming, 13:1 (2012), 290–297

[4] N.S. Boaster, N.P. Zhidkov, G.M. Kobelkov, Numerical Methods, Lab Basic Knowledge, 2003, 632 pp.

[5] O.A. Ladyzhenskaya, V.A. Solonnikov, N.N. Ural’tseva, Linear and Quasi-Linear Parabolic Equation, Nauka, M., 1967, 736 pp.

[6] V.T. Pinkevich, “On the order of the remainder term of the Fourier series of functions differentiable in the sense of Weyl’ya”, Math. USSR Academy of Sciences . Ser . Mat., 4:6 (1940), 521–528

[7] A.A. Samarskii, The Theory of Difference Schemes, Nauka, M., 1989, 432 pp.

[8] A.I. Sukhinov, A.E. Chistyakov, A.V. Shishenya, “Error Estimate for Diffusion Equations Solved by Schemes with Weights”, Mathematical Models and Computer Simulations, 6:3 (2014), 324–331 | DOI

[9] R.V. Zhalnin, N.V. Zmitrenko, M.E. Ladonkina, V.F. Tishkin, “Numerical Simulation of Richtmyer - Meshkov Using Schemes of High Order of Accuracy”, Mathematical Simulation, 19:10 (2007), 61–66

[10] A.I. Sukhinov, A.E. Chistyakov, E.A. Protsenko, “Mathematical Modeling of Sediment Transport in the Coastal Zone of Shallow Reservoirs”, Mathematical Models and Computer Simulations, 6:4 (2014), 351–363 | DOI

[11] A.I. Sukhinov, A.E. Chistyakov, E.A. Protsenko, “Mathematical Modeling of Sediment Transport in Coastal Water Systems to Multiprocessor Computer System”, Computational Methods and Programming, 15:4 (2014), 610–620

[12] V.S. Vladimirov, Equations of Mathematical Physics, Nauka, M., 1988, 512 pp.

[13] A.I. Sukhinov , A.V. Nikitina, A.E. Chistyakov, I.S. Semenov, “Mathematical Modeling of the Formation of Zamora in Shallow Waters on a Multiprocessor Computer System”, Computational methods and programming, 14:1 (2013), 103–112

[14] A.I. Sukhinov, A.V. Nikitina, A.E. Chistyakov, “Numerical Simulation of Biological Remediation Azov Sea”, Mathematical Simulation, 24:9 (2012), 3–21

[15] A.S. Antonov, I.L. Artemyev, A.V. Boukhanovsky etc., “The Project «Supercomputer Education»: 2012”, Bulletin of the Nizhny Novgorod University of N.I. Lobachevsky, 1:1 (2013), 12–16

[16] V.V. Voevodin, V.P. Gergel, L.B. Sokolinskii etc., “Development of Supercomputer Education in Russia: Current Results and Prospects”, Bulletin of the Nizhny Novgorod University of N.I. Lobachevsky, 4:1 (2012), 268–274

[17] A.S. Antonov, I.L. Artemyev, A.V. Boukhanovsky etc., “The project «Supercomputer Education»: 2012”, Scientific Service on the Internet: The Search for New Solutions Proceedings of the International Supercomputer Conference (Moscow), 2012, 4–8