A spatial generalization of the method of conformal mappings for the solution of model boundary-value filtration problems
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We propose a mathematical model for the calculation of the ideal flow in a curvilinear parallelepiped bounded by the stream surfaces and the equipotential ones. We suggest the system of second-order partial differential equations, which relates the potential and the stream functions spatially complexconjugate to it. On this basis, we formulate the problem of finding the spatial conformal mapping of a curvilinear parallelepiped on a rectangular parallelepiped and the corresponding inverse problem (of finding the inverse conformal mapping). An algorithm of solution of the problem is constructed, and the numerical calculations are carried out.
- A. Ya. Bomba, V. M. Bulavats’kyi, and V. V. Skopets’kyi, Nonlinear Mathematical Models of Processes of Geohydrodynamics [in Ukrainian], Naukova Dumka, Kiev (2007).
- A. Ya. Bomba and A. V. Terebus, “Modeling of ideal fields for thin spatially curved strata,” Mat. Komp. Model. Ser. Fiz.-Mat. Nauk, Issue 4, 31–40 (2010).
- A. Ya. Bomba and A. V. Terebus, “Modeling of quasiideal fields for thin spatially curved strata,” Zh. Obchysl. Prikl. Mat., No. 4, 9–16 (2010).
- O. V. Golubeva, Course of Mechanics of Continua [in Russian], Vysshaya Shkola, Moscow (1972).
- V. I. Eliseev, Introduction to Methods of the Theory of Functions of Spatial Complex Variable [in Russian], NIAT, Moscow (1990).
- Yu. E. Klymyuk and D. O. Prygornyts’kyi, “Numerical solution of inverse boundary-value problems with spatial conformal mappings of curvilinear parallelepipeds onto rectangular ones,” Volyn. Mat. Visn. Ser. Prikl. Mat., 5(14), 104–143 (2008).
- V. A. Tolpaev, Mathematical Models of Two-Dimensional Filtration in Anisotropic, Inhomogeneous, and Multilayer Media [in Russian], Author’s Abstract of the Doctoral Degree Thesis (Phys.-Math. Sci.), Stavropol’ (2004).
- V. A. Tolpaev and V. V. Paliev, “The equation of continuity in two-dimensional models of filtration of fluids and gases in curved strata with finite thickness,” Izv. Sarat. Univ. Ser. Mat. Mekh. Inf., 7, Issue 2, 49–53 (2007).
- T. V. Hromadka and R. J. Whitley, “Approximating three-dimensional steady-state potential flow problems using two-dimensional complex polynomials,” Eng. Anal. Bound. Elem., 29, No. 2, 190–194 (2005). CrossRef
- W. Koppenfels and F. Stallmann, Praxis der Konformen Abbildung, Springer, Berlin (1959). CrossRef
- E. D. Martin, “Some elements of a theory of multidimensional complex variables: Part I. General theory,” J. Franklin Inst., 326, No. 5, 611–647 (1989). CrossRef
- W. T. Shaw, Complex Variable Methods for 3D Applied Mathematics: 3D Twistors and the Biharmonic Equation, arXiv:submit/0045479 [physics.flu-dyn] 23 May 2010.
- A spatial generalization of the method of conformal mappings for the solution of model boundary-value filtration problems
Journal of Mathematical Sciences
Volume 187, Issue 5 , pp 596-605
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