The general purpose system for construction of two–dimensional orthogonal grids
Matematičeskoe modelirovanie, Tome 29 (2017) no. 11, pp. 71-88.

Voir la notice de l'article provenant de la source Math-Net.Ru

The general purpose service system generation of two–dimensional orthogonal grids for numerical modeling of physical processes systems operation is described. The algorithm of numerical conformal mapping of an arbitrary simply connected region to parametric rectangle, which lies at its core, is described. The methods of testing and examples of conformal mappings are considered. Also the correspondence with the experimental data for the hydrodynamics and applications to the optimization of flows in complex configuration channels are illustrated.
Mots-clés : оrthogonal grid
Keywords: conformal mapping, finite element method.
@article{MM_2017_29_11_a4,
     author = {V. S. Goun and V. S. Morozova and V. L. Polyatsko},
     title = {The general purpose system for construction of two{\textendash}dimensional orthogonal grids},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {71--88},
     publisher = {mathdoc},
     volume = {29},
     number = {11},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_11_a4/}
}
TY  - JOUR
AU  - V. S. Goun
AU  - V. S. Morozova
AU  - V. L. Polyatsko
TI  - The general purpose system for construction of two–dimensional orthogonal grids
JO  - Matematičeskoe modelirovanie
PY  - 2017
SP  - 71
EP  - 88
VL  - 29
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2017_29_11_a4/
LA  - ru
ID  - MM_2017_29_11_a4
ER  - 
%0 Journal Article
%A V. S. Goun
%A V. S. Morozova
%A V. L. Polyatsko
%T The general purpose system for construction of two–dimensional orthogonal grids
%J Matematičeskoe modelirovanie
%D 2017
%P 71-88
%V 29
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2017_29_11_a4/
%G ru
%F MM_2017_29_11_a4
V. S. Goun; V. S. Morozova; V. L. Polyatsko. The general purpose system for construction of two–dimensional orthogonal grids. Matematičeskoe modelirovanie, Tome 29 (2017) no. 11, pp. 71-88. http://geodesic.mathdoc.fr/item/MM_2017_29_11_a4/

[1] J. F. Thompson, B. Soni, N. Weaterill (eds.), Handbook of grid generation, CRC Press, NY, 1998, 1097 pp. | MR

[2] G. Strang, G. Fix, An Analysis of the Finite Element Method, Series in Automatic Computation, Prentice-Hall Inc., Englewood Clifs, N.J., 1973, xiv+306 pp. | MR | Zbl

[3] S.K. Godunov, G. P. Prokopov, “The use of moving meshes in gas-dynamics calculations”, USSR Computational Mathematics and Mathematical Physics, 12:2 (1972), 182–195 | DOI | MR | Zbl

[4] S.K. Godunov, A.V. Zabrodin, M.Ya. Ivanov, A.N. Kraiko, G.P. Prokopov, Chislennoe reshenie mnogomernyh zadach gazovoj dinamiki, Nauka, M., 1976, 400 pp.

[5] S.A. Ivanenko, G. P. Prokopov, “Methods of Adaptive Harmonic Grid Generation”, Computational Mathematics and Mathematical Physics, 37:6 (1997), 627–645 | MR | Zbl

[6] G.P. Prokopov, Postroenie ortogonalnykh raznostnykh setok posredstvom rascheta konformnykh otobrazheniy, Preprint No 45, IPM AN SSSR, M., 1970

[7] G.P. Prokopov, O raschete raznostnykh setok, blizkikh k ortogonalnym v oblastyakh s krivolineynymi granitsami, Preprint No 17, IPM AN SSSR, M., 1974

[8] A.M. Winslow, “Numerical solution of quasilinear Poisson equation in nonuniform triangle mesh”, J. Comp. Phys., 1:2 (1966), 149–172 | DOI | MR | Zbl

[9] S.K. Godunov, G. P. Prokopov, “On the computational of conformal transformations and the construction of difference meshes”, USSR Computational Mathematics and Mathematical Physics, 7:5 (1967), 89–124 | DOI | MR | Zbl

[10] G.P. Prokopov, “Nekotorye obshchie voprosy konstruirovaniya algoritmov postroeniya raznostnykh setok”, Voprosy Atomnoy Nauki i Tekhniki. Matematicheskoe modelirovanie fizicheskih processov, 1988, no. 1, 3–13

[11] V.D. Liseykin, “A survey of methods for constructing structured adaptive grids”, USSR Computational Mathematics and Mathematical Physics, 36:1 (1996), 3–41

[12] G.P. Prokopov, “Vibor parametrov pri variatsionnom podkhode k raschetu regularnykh setok”, Keldysh Institute preprints, 2006, 014, 32 pp.

[13] G.P. Prokopov, “Realizatsiya variatsionnogo podkhoda k raschetu dvumernikh setok v nestatsionarnykh zadachakh”, Keldysh Institute preprints, 2005, 116, 36 pp.

[14] G.P. Prokopov, “Variatsionnye metody rascheta dvumernikh setok pri reshenii nestatsionarnykh zadach”, Keldysh Institute preprints, 2003, 004, 32 pp.

[15] G.P. Prokopov, “Universalnye variatsionnye funktsionaly dlya postroeniya dvumernikh setok”, Keldysh Institute preprints, 2001, 001

[16] R.N. Antonova, G.P. Prokopov, “Raschet kvaziortogonalnykh setok minimizatsiey variatsionnykh funktsionalov”, Keldysh Institute preprints, 1998, 031 | Zbl

[17] G.P. Prokopov, “Metodologiya variatsionnogo podkhoda k postroeniyu kvaziortogonalnykh setok”, Voprosy Atomnoy Nauki i Tekhniki. Matematicheskoe modelirovanie fizicheskih processov, 1998, no. 1, 37–46

[18] R.N. Antonova, G.P. Prokopov, “Raschet gladkikh slozhnosostavnikh setok pryamoi minimizatsiey variatsionnykh funktsionalov”, Voprosy Atomnoy Nauki i Tekhniki. Matematicheskoe modelirovanie fizicheskih processov, 1997, no. 2, 17–24

[19] R.N. Antonova, G.P. Prokopov, O.I. Sofronova, “Raschet podvizhnikh raznostnikh setok i problema nachalnogo priblizhiniya dlya setki v slozhnoy oblasti”, Voprosy Atomnoy Nauki i Tekhniki. Matematicheskoe modelirovanie fizicheskih processov, 1996, no. 1–2, 84–90

[20] G.P. Prokopov, O.I. Sofronova, “Organizatsiya raschetov gladkikh setok v slozhnosostavnikh oblastyakh”, Voprosy Atomnoy Nauki i Tekhniki. Matematicheskoe modelirovanie fizicheskih processov, 1996, no. 3, 9–17

[21] R.N. Antonova, G.P. Prokopov, “Sravnenie neskolkikh variantov postroeniy dvumernykh raznostnykh setok posredstvom interpolyatsionnykh formul”, Voprosy Atomnoy Nauki i Tekhniki. Matematicheskoe modelirovanie fizicheskih processov, 1994, no. 1, 78–84

[22] G.P. Prokopov, “Konstruirovanie testovikh zadach dlya postroeniya regulyarnykh setok”, Voprosy Atomnoy Nauki i Tekhniki. Matematicheskoe modelirovanie fizicheskih processov, 1993, no. 1, 7–13

[23] G.P. Prokopov, “Postroenie raznostnykh setok putem optimizatsii parametrov interpolyatsii formul”, Voprosy Atomnoy Nauki i Tekhniki. Matematicheskoe modelirovanie fizicheskih processov, 1990, no. 1, 7–16

[24] G.P. Prokopov, “Ob organizatsii sravneniya algoritmov I programm postroeniya regulyarnikh dvumernikh raznostnikh setok”, Voprosy Atomnoy Nauki i Tekhniki. Matematicheskoe modelirovanie fizicheskih processov, 1989, no. 3, 98–108

[25] D. Gaier, “Ermittlung des konformen Moduls von Vierecken mit Differenzenmethoden”, Numerische Mathematik, 19 (1972), 179–194 | DOI | MR | Zbl

[26] J. Weisel, “Numerische Ermittlung quasikonformer Abbildungen mit finiten Elemente”, Numerische Mathematik, 35 (1980), 201–222 | DOI | MR | Zbl

[27] A. Ia. Gun, G. Ia. Gun, “Konformnoe otobrazhenie proizvolnogo chetyrekhugolnika na priamougolnik”, Izvestiia vysshikh uchebnikh zavedenii. Chernaia metallurgiia, 1982, no. 1, 152

[28] J. Weisel, “Losung singularer Variationsprobleme durch die Verfahren von Ritz und Galerkin mit finiten Elementen”, Anwendungen in der konformen Abbildung. Mitt. Math. Sem. Giessen, 1979, 156 | MR | Zbl

[29] J. Tri Quach, Numerical conformal mappings and capacity computation, Master's Thesis, University of Helsinki. Faculty of Science. Department of Mathematics and Statistics, 2007, 79 pp.

[30] N. Papamichael, Lectures on Numerical Conformal Mapping, Department of Mathematics and Statistics. University of Cyprus, 2008, 225 | MR

[31] M.A. Lavrentev, B.V. Shabat, Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1973, 736 pp.

[32] V.S. Gun, V.S. Morozova, V.L. Poliatsko, “Matematicheskoe modelirovanie techeniia topliva v kanalakh konusa raspylitelia”, Vestnik Iuzhnouralskogo gosudarstvennogo universiteta. Seriia: Mashinostroenie, 13:2 (2013), 74–78

[33] O.C. Zienkiewichz, The finite element method in engineering science, McGrow-Hill, London, 1971, 539 pp. | MR

[34] V.S. Kuznetsov, A.S. Shablovskiy, G.A. Troshin, “Experimental study of the hydrodynamic parameters of liquid flow in the throttle channel”, El. Sc.-Tech. Publ. “Science and Education” of Bauman MSTU, 2011, no. 10 (in Russ.) (accessed 07.07.2014) http://technomag.edu.ru/doc/230378.html

[35] V.S. Gun, V.S. Morozova, V.L. Polyacko, “Mathematical Modeling of Fuel Flow in Channels Cone Spray”, Proc. Engineering, 129 (2015), 145–150 | DOI

[36] L.V. Grekhov, N.A. Ivashchenko, V.A. Markov, Toplivnaia apparatura i sistemy upravleniia dizelei, Uchebnik dliia VUZov, Legion-Avtodata, M., 2004, 344 pp.