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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 7, Pages 1147–1163 (Mi zvmmf10751)  

Estimation of two error components in the numerical solution to the problem of nonisothermal flow of polymer fluid between two coaxial cylinders

A. M. Blokhinab, E. A. Kruglovac, B. V. Semisalovc

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

Abstract: An algorithm for solving a stationary nonlinear problem of a nonisothermal flow of an incompressible viscoelastic polymer fluid between two coaxial cylinders is developed on the basis of Chebyshev approximations and the collocation method. In test calculations, the absence of saturation of the algorithm is shown. A posteriori estimates of two error components in the numerical solution—the error of approximation method and the round-off error—are obtained. The behavior of these components as a function of the number of nodes in the spatial grid of the algorithm and the radius of the inner cylinder is analyzed. The calculations show exponential convergence, stability to rounding errors, and high time efficiency of the algorithm developed.

Key words: polymer fluid dynamics, algorithm without saturation, Chebyshev polynomials, collocation method, error estimates, exponential convergence.

Funding Agency Grant Number
Russian Science Foundation 17-71-10135


DOI: https://doi.org/10.31857/S004446690001462-9

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:7, 1099–1115

Bibliographic databases:

UDC: 519.635
Received: 24.10.2017
Revised: 08.12.2017

Citation: A. M. Blokhin, E. A. Kruglova, B. V. Semisalov, “Estimation of two error components in the numerical solution to the problem of nonisothermal flow of polymer fluid between two coaxial cylinders”, Zh. Vychisl. Mat. Mat. Fiz., 58:7 (2018), 1147–1163; Comput. Math. Math. Phys., 58:7 (2018), 1099–1115

Citation in format AMSBIB
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\paper Estimation of two error components in the numerical solution to the problem of nonisothermal flow of polymer fluid between two coaxial cylinders
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2018
\vol 58
\issue 7
\pages 1147--1163
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\crossref{https://doi.org/10.31857/S004446690001462-9}
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