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.

PY - 2025

Y1 - 2025

N2 - Abstract: For equations of the rheological mesoscopic Vinogradov-Pokrovskii model the boundary value problem is formulated that describes non-isothermal Poiseuille-type ows of a viscoelastic polymer uid 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 nite-di erence scheme for the time marching. The analysis of distributions of the uid's velocity and temperature in the channel, as well as, of the time dependencies of uid's ow 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 Semisalov, B.V., Bugoets, I.A., Kutkin, L.I. Simulation of the nonstationary non-isothermal polymer fluid flow through the channel with elliptic cross-section associates with the destruction (the stability loss) of a Poiseuille type ow.

AB - Abstract: For equations of the rheological mesoscopic Vinogradov-Pokrovskii model the boundary value problem is formulated that describes non-isothermal Poiseuille-type ows of a viscoelastic polymer uid 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 nite-di erence scheme for the time marching. The analysis of distributions of the uid's velocity and temperature in the channel, as well as, of the time dependencies of uid's ow 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 Semisalov, B.V., Bugoets, I.A., Kutkin, L.I. Simulation of the nonstationary non-isothermal polymer fluid flow through the channel with elliptic cross-section associates with the destruction (the stability loss) of a Poiseuille type ow.

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

U2 - 10.33048/semi.2025.22.018

DO - 10.33048/semi.2025.22.018

M3 - статья

VL - 22

SP - 252

EP - 5273

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 1

ER -