Расчёт нестационарного неизотермического течения полимерной жидкости в канале с эллиптическим сечением

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Расчёт нестационарного неизотермического течения полимерной жидкости в канале с эллиптическим сечением. / Семисалов, Борис Владимирович; Бугоец, Иван Андреевич; Куткин, Лев Ильич.

In: Сибирские электронные математические известия, Vol. 22, No. 1, 2025, p. 252-273.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{bcf49deef6ce445d9405864ac495db8d,

title = "Расчёт нестационарного неизотермического течения полимерной жидкости в канале с эллиптическим сечением",

abstract = "For equations of the rheological mesoscopic Vinogradov- Pokrovskii model the boundary value problem is formulated that describes non-isothermal Poiseuille-type flows of a viscoelastic polymer fluid through the channel with the elliptic cross-section under the condition that the pressure gradient and the temperature of the channel{\textquoteright}s wall undergo rapid (impulse) changes. To solve the problem, we develop the numerical algorithm based on the collocation method, the application of polynomial and rational approximations with respect to spatial variables and of finite-difference scheme for the time marching. The analysis of distributions of the fluid{\textquoteright}s velocity and temperature in the channel, as well as, of the time dependencies of fluid{\textquoteright}s flow and mean temperature is performed. The critical relations between the amplitudes and durations of impulses of the pressure gradient and of the temperature are computed. They are those values surpassing which leads to the divergence of the numerical solution that, as we suppose, can be associates with the destruction (the stability loss) of a Poiseuilletype flow.",

keywords = "Poiseuille-type flow, accounting for singularities of the solution, channel with elliptic cross-section, critical relations of the parameters, destruction of the flow, highly-accurate algorithm, impulse impact, mesoscopic model, polymer fluid",

author = "Семисалов, {Борис Владимирович} and Бугоец, {Иван Андреевич} and Куткин, {Лев Ильич}",

note = " 075-15-2022-281. Расчёт нестационарного неизотермического течения полимерной жидкости в канале с эллиптическим сечением / Б. В. Семисалов, И. А. Бугоец, Л. И. Куткин // Сибирские электронные математические известия. – 2025. – Т. 22, № 1. – С. 252-273. – DOI 10.33048/semi.2025.22.018",

year = "2025",

doi = "10.33048/semi.2025.22.018",

language = "русский",

volume = "22",

pages = "252--273",

journal = "Сибирские электронные математические известия",

issn = "1813-3304",

publisher = "Sobolev Institute of Mathematics",

number = "1",

}

RIS

TY - JOUR

T1 - Расчёт нестационарного неизотермического течения полимерной жидкости в канале с эллиптическим сечением

AU - Семисалов, Борис Владимирович

AU - Бугоец, Иван Андреевич

AU - Куткин, Лев Ильич

N1 - 075-15-2022-281. Расчёт нестационарного неизотермического течения полимерной жидкости в канале с эллиптическим сечением / Б. В. Семисалов, И. А. Бугоец, Л. И. Куткин // Сибирские электронные математические известия. – 2025. – Т. 22, № 1. – С. 252-273. – DOI 10.33048/semi.2025.22.018

PY - 2025

Y1 - 2025

N2 - For equations of the rheological mesoscopic Vinogradov- Pokrovskii model the boundary value problem is formulated that describes non-isothermal Poiseuille-type flows of a viscoelastic polymer fluid through the channel with the elliptic cross-section under the condition that the pressure gradient and the temperature of the channel’s wall undergo rapid (impulse) changes. To solve the problem, we develop the numerical algorithm based on the collocation method, the application of polynomial and rational approximations with respect to spatial variables and of finite-difference scheme for the time marching. The analysis of distributions of the fluid’s velocity and temperature in the channel, as well as, of the time dependencies of fluid’s flow and mean temperature is performed. The critical relations between the amplitudes and durations of impulses of the pressure gradient and of the temperature are computed. They are those values surpassing which leads to the divergence of the numerical solution that, as we suppose, can be associates with the destruction (the stability loss) of a Poiseuilletype flow.

AB - For equations of the rheological mesoscopic Vinogradov- Pokrovskii model the boundary value problem is formulated that describes non-isothermal Poiseuille-type flows of a viscoelastic polymer fluid through the channel with the elliptic cross-section under the condition that the pressure gradient and the temperature of the channel’s wall undergo rapid (impulse) changes. To solve the problem, we develop the numerical algorithm based on the collocation method, the application of polynomial and rational approximations with respect to spatial variables and of finite-difference scheme for the time marching. The analysis of distributions of the fluid’s velocity and temperature in the channel, as well as, of the time dependencies of fluid’s flow and mean temperature is performed. The critical relations between the amplitudes and durations of impulses of the pressure gradient and of the temperature are computed. They are those values surpassing which leads to the divergence of the numerical solution that, as we suppose, can be associates with the destruction (the stability loss) of a Poiseuilletype flow.

KW - Poiseuille-type flow

KW - accounting for singularities of the solution

KW - channel with elliptic cross-section

KW - critical relations of the parameters

KW - destruction of the flow

KW - highly-accurate algorithm

KW - impulse impact

KW - mesoscopic model

KW - polymer fluid

UR - https://math-semr.ru/sites/math-semr.ru/files/2025-04/p0252-0273.pdf

UR - https://www.mendeley.com/catalogue/27bc5fca-c908-3a62-b932-93915a6913c7/

U2 - 10.33048/semi.2025.22.018

DO - 10.33048/semi.2025.22.018

M3 - статья

VL - 22

SP - 252

EP - 273

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 1

ER -

ID: 71567886