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On one method for constructing a dynamical mesh of nonlinear quasiperfect processes in deformable anisotropic media

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Języki publikacji
EN
Abstrakty
EN
A new algorithm has been developed for numerical solving inverse nonlinear boundary value problems on quasiconformal mapping in anisotropic media, which are curvilinear tetragons limited by lines of a flow and equipotential lines under action of a potential gradient tensor. The dynamical mesh has been constructed and the velocity field of the domain has been calculated.
Rocznik
Strony
7--21
Opis fizyczny
Bibliogr. 34 poz.
Twórcy
autor
  • Faculty of Computer Science and Applied Mathematics, Departament of Mathematics and Computer Science, Rivne State Humanitarian University, Ostafov Str. 31, Rivne 33028 Ukraine
autor
  • Faculty of Computer Science and Applied Mathematics, Departament of Mathematics and Computer Science, Rivne State Humanitarian University, Ostafov Str. 31, Rivne 33028 Ukraine
Bibliografia
  • [1] Bomba A.Y., Kashtan S.S.: Numerical Decision of Inverse Nonlinear Marginal Problems on Conformal and AS-Conformal Displaying, Volyn Mathematical Bulletin, 2001, v. 8, pp. 10-23.
  • [2] Bomba A.Y., Kashtan S.S.: About Nonlinear Revisins of Boundary Value Problems on Conformal Mappings in Multiply Connected Areas, // Visnyk of the Lviv University. Ser. Applied Mathematics and Computer Science, 2000, No. 2, pp. 3-15.
  • [3] Bomba A.Y., Kashtan S.S.: About Solving One Class Nonlinear Inverted Boundary Value Problems on Conformal Reflections, Volyn Mathematical Bulletin, 1999, v. 6, pp.25-36.
  • [4] Bomba A.Y., Kashtan S.S., Kuzmenko A.P.: About Usage of Summary Representation Method for Solving Nonlinear Inverted Boundary Value Problems on Conformal Reflections, Volyn Mathematical Bulletin, 1998, v.5, pp.16-25.
  • [5] Bomba A.Y, Prigornitsky D.O.: Numerical Solving of Inverse Nonlinear Boundary Value Problems on Conformal and Quasiconformal Mappings in Double- Connected Areas, Bulletin of the University of Kiev. Series of Physics & Mathematics, 2001, No. 3, pp.151-158.
  • [6] Bomba A.Y., Kashtan S.S.: Nonlinear Referencing the Boundary Value Problems on Quasiconformal Mappings in Anisotropic Ambiences, Bulletin of the University of Kiev. Series: Physics & Mathematics, 2001, No. 4, pp.160-174.
  • [7] Khlapuk M.M., Bomba A.Y., Sydorchuk B.P.: On Modelling Interaction between Filtration and Mechanical suffusion. [In:] Problems of Filtration Theory, Rivne, 1998, pp. 157-166.
  • [8] Bomba A.Y., Khlapuk M.M., Sydorchuk B.P.: Mathematical Modelling Nonlinear Filtration Processes Allowing for Small Deformation of a Medium, Actual Problems of Water Economy, 1997, v. l,pp. 11-15.
  • [9] Bomba A.Y., Khlapuk M.M., Sydorchuk B.P.: On Modelling and Solving Ove Class of Locally Perturbed Nonlinear Problems, Volyn Mathematical Bulletin, 1995, v. 2, pp. 22-25.
  • [10] Bomba A.Y., Khlapuk M.M., Sydorchuk B.P.: Modelling Interaction between Gradients and Filtrate Medium and Problems of Dispersive Systems Stability, Physics of Condense High-Molecular Systems. Scientifis Transactions of Rivne Pedagogical Institute, 1997, v. 3, pp. 202-207.
  • [11] Lyashko I.I., Velikoivanenko I.M., Lavrik V.I., Mistetsky G.E.: Method of Majorizing Regions in Theory of Filtration. Naukova Dumka, Kyiv 1980.
  • [12] Marchuk G.I.: Methods of Numerical Mathematics, Naukova Dumka, Kyiv 1980.
  • [13] Samarsky A. A.: Theory of Difference Schemes, Nauka, Moscow 1977.
  • [14] Vlasyuk A.P., Mikhalchuk V.G.: Automatic Construction of Conformal and Quasiconformal Mappings of Tetraangular Regions by Difference Grid with “Floating” Nodes, Preprint by Institute of Mathematics, UNAS, Kyiv, 1989, No. 89. 79, p. 55.
  • [15] Vlasyuk A.P., Mikhalchuk V.G.: Automatic Construction of Conformal and Quasiconformal Mappings of Two- and Three-Connected Regions, Preprint by Institute of Mathematics, UNAS, Kyiv, 1991, No. 91. 57, p. 56.
  • [16] Godunov S.K., Prokopov G.P.: About Calculations of Conformal Mappings and Construction of Difference Meshs, Journal of Numerical Mathematics and Mathematical Physics, 1967, v. 7, No.5, pp. 1031-1059.
  • [17] Godunov S.K., Prokopov G.P. About Using Moving Grids in Gas-Dynamic Calculations, Journal of Numerical Mathematics and Mathematical Physics, 1972, v. 12, No. 2, pp.429-440.
  • [18] Numerical Conformal Mapping, J. Comput. and Applied. Math., 1986, No. 14, pp. 1-369.
  • [19] Ortega D., Reinboldt V.: Iteration Methods od Solving Nonlinear Sets of Equations with Many Uknowns, Mir, Moscow 1975.
  • [20] Polubarinova-Kochinova P.Y.: Theory of Ground Water Motion, Gostechizdat, Moscow 1952.
  • [21] Development of Investigation in Filtration Theory in Ussr (1917-1967) / By ed. Polubarinova-Kochinova P.Y., Nauka, Moscow 1969.
  • [22] Lavrentiev M.A., Shabat B.V.: Methods of Theory of a Complex Variable Function, Nauka, Moscow 1973.
  • [23] Aravin V.I., Numerov S.N.: Theory of Liquids anf Gases Motion in an Undeformable Porous Medium, GITTL, Moscow 1953.
  • [24] Slezkin H.A.: About Differential Equations of Filtration, Reports of Academy of Sciences of USSR, 1951, v. 79, No. 5, pp. 755-758.
  • [25] Nikolayevsky V.N. Convective Diffision in Porous Media, Applied Mathematics and Mechanics, 1959, v. 23, No. 6, pp. 1042-1050.
  • [26] Gavrilko V.M., Alekseyev V.S.: Filters of Drilling Holes, Nedra, Moscow 1985.
  • [27] Chugayev R.R. Calculating Schemes of Capillarity Phenomenon in Soils, News of VNIIG, 1949, v. 39.
  • [28] Khristiyanovich S.A., Mikhlin S.G., Devison B.B.: Some New Questions of Solids Mechanics, Publ. AS of USSR, Moscow 1939.
  • [29] Darcy H.: Les fontains publiques de la ville de Dijon, Paris, 1856.
  • [30] Dupuit J.: Études theoriques sur le monvement des eaux dans les canaux decouverts et atravers les terrains perméables Dunon. 2 éd., Paris 1863.
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  • [32] Sergiyenko I.V., Skopetsky V.V., Deyneka V.S.: Mathematical Modelling and Studying Processes in Nonhomogeneous Media, Naukova Dumka, Kyiv 1991.
  • [33] Deyneka V.S., Sergiyenko I.V., Skopetsky V.V.: Models and Methods for Solving Problems with Conjugation Conditions, Naukova Dumka, Kyiv 1998.
  • [34] Savula Y., Shynkarenko G.A., Vovk V.N.: Some Applications of Finite Elements Method, Preprint by Lviv University, Lviv, 1981, p. 38
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD7-0027-0077
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