Narmuradov, C. B., Toyirov, A. X., Yuldashev, S. M., & Xolliev, F. B.
Mathematical modeling of movement of a viscous incompressible liquid by the spectral-grid method. |
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Full Article: PDF
Scientific Object Identifier: http://s-o-i.org/1.1/TAS-04-84-44
DOI: https://dx.doi.org/10.15863/TAS.2020.04.84.44
Language: English
Citation: Narmuradov, C. B., Toyirov, A. X., Yuldashev, S. M., & Xolliev, F. B. (2020). Mathematical modeling of movement of a viscous incompressible liquid by the spectral-grid method. ISJ Theoretical & Applied Science, 04 (84), 252-260. Soi: http://s-o-i.org/1.1/TAS-04-84-44 Doi: https://dx.doi.org/10.15863/TAS.2020.04.84.44 |
Pages: 252-260
Published: 30.04.2020
Abstract: The article analyzes the existing numerical methods for solving the hydrodynamic stability problem. We consider such methods as: finite-difference, step-by-step integration, local collocation, determinant, pre-integration method, spectral, spectral-grid. The spectral-grid method was used for mathematical modeling of the problem by stability hydrodynamics, the results obtained allow us to establish the convergence of the spectral-grid method, estimate the convergence rate and develop an effective algorithm that significantly reduces the order of complex matrices in the algebraic system being solved in comparison with the known spectral methods.
Key words: hydrodynamic stability, Reynolds number, wave numbers, eigenvalues and eigenvectors, Chebyshev polynomials of the first kind, conditions of orthogonality and continuity, grave conditions, generalized and standard eigenvalue problem, complex matrices.
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