Khujaev, J., Shaimov, K., & Shafiyev, T.
Application of the differential-difference method for solving the problems about the current of the incompressible liquid in the rectangular area at the small numbers of the Reinolds. |
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Full Article: PDF
Scientific Object Identifier: http://s-o-i.org/1.1/TAS-10-66-5
DOI: https://dx.doi.org/10.15863/TAS.2018.10.66.5
Language: Russian
Citation: Khujaev, J., Shaimov, K., & Shafiyev, T. (2018). Application of the differential-difference method for solving the problems about the current of the incompressible liquid in the rectangular area at the small numbers of the Reinolds. ISJ Theoretical & Applied Science, 10 (66), 37-44. Soi: http://s-o-i.org/1.1/TAS-10-66-5 Doi: https://dx.doi.org/10.15863/TAS.2018.10.66.5 |
Pages: 37-44
Published: 30.10.2018
Abstract: In this paper, we propose a method of applying the method of lines, which has been developed in detail for the Dirichlet problem, in solving two-dimensional problems of hydrodynamics. The advantage of the method is to exclude the input of fictitious time in solving the equations of the current and pressure function, since finite-difference equations with respect to two Cartesian coordinates are solved simultaneously and accurately. The structure of the main tridiagonal matrices of the transition to finite difference equations remains the same for the case of using separate equations of the stream function, vorticity, and pressure. For the exact solution of finite-difference equations, the eigenvalues and vectors of the basic transition matrix are attracted, the values of the elements of which are calculated only once.
Key words: Navier-Stokes equations and continuity, velocities in coordinates, pressure, stream function, vorticity, finite-difference method, matrix representation of finite-difference equations, diagonalization, transition formulas.
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