Numerical Analysis of the Blow-Up of One-Dimensional Polymer Fluid Flow with a Front Full article
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Computational Mathematics and Mathematical Physics
ISSN: 0965-5425 , E-ISSN: 1555-6662 |
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| Output data | Year: 2024, Volume: 64, Number: 1, Pages: 151-165 Pages count : 15 DOI: 10.1134/s0965542524010068 | ||||||
| Tags | polymer fluid, rheology, mesoscopic model, one-dimensional flow, Burgers equation, rational approximation, Chebyshev–Padé approximation, trajectory of a singular point in the complex plane | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 23-21-00499 |
Abstract:
One-dimensional flows of an incompressible viscoelastic polymer fluid that are qualitatively similar to the solutions of Burgers’ equation are described on the basis of mesoscopic approach for the first time. The corresponding initial boundary-value problem is posed for the system of quasilinear differential equations. The numerical algorithm for solving it is designed and verified. The algorithm uses the explicit fifth-order scheme to approximate unknown functions with respect to time variable and the rational barycentric interpolations with respect to space variable. A method for localization of singular points of the solution in the complex plain and for adaptation of the spatial grid to them is implemented using the Chebyshev-Padé approximations. Two regimes of evolution of the solution to the problem are discovered and characterized while using the algorithm: regime 1—a smooth solution exists in a sufficiently large time interval (the singular point moves parallel to the real axis in the complex plane); regime 2—the smooth solution blows up at the beginning of evolution (the singular point reaches the segment of the real axis where the problem is posed). We study the influence of the rheological parameters of fluid on the realizability of these regimes and on the length of time interval where the smooth solution exists. The obtained results are important for the analysis of laminar-turbulent transitions in viscoelastic polymer continua.
Cite:
Bryndin L.S.
, Semisalov B.V.
, Beliaev V.A.
, Shapeev V.P.
Numerical Analysis of the Blow-Up of One-Dimensional Polymer Fluid Flow with a Front
Computational Mathematics and Mathematical Physics. 2024. V.64. N1. P.151-165. DOI: 10.1134/s0965542524010068 WOS Scopus РИНЦ РИНЦ OpenAlex
Numerical Analysis of the Blow-Up of One-Dimensional Polymer Fluid Flow with a Front
Computational Mathematics and Mathematical Physics. 2024. V.64. N1. P.151-165. DOI: 10.1134/s0965542524010068 WOS Scopus РИНЦ РИНЦ OpenAlex
Original:
Брындин Л.С.
, Семисалов Б.В.
, Беляев В.А.
, Шапеев В.П.
Численный анализ разрушения одномерного течения полимерной жидкости с фронтом
Журнал вычислительной математики и математической физики. 2024. Т.64. №1. С.162-175. DOI: 10.31857/S0044466924010126 РИНЦ OpenAlex
Численный анализ разрушения одномерного течения полимерной жидкости с фронтом
Журнал вычислительной математики и математической физики. 2024. Т.64. №1. С.162-175. DOI: 10.31857/S0044466924010126 РИНЦ OpenAlex
Dates:
| Submitted: | Mar 21, 2023 |
| Accepted: | Sep 16, 2023 |
| Published print: | Mar 21, 2024 |
| Published online: | Mar 21, 2024 |
Identifiers:
| Web of science: | WOS:001187462000007 |
| Scopus: | 2-s2.0-85188231065 |
| Elibrary: | 66468709 | 67306764 |
| OpenAlex: | W4393059694 |