Numerical Analysis of Stability Loss for Poiseuille-Type Polymer Fluid Flows under the Pulsed Effect of Pressure and Temperature

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Numerical Analysis of Stability Loss for Poiseuille-Type Polymer Fluid Flows under the Pulsed Effect of Pressure and Temperature. / Semisalov, B. V.; Bugoets, I. A.; Kutkin, L. I. et al.

In: Computational Mathematics and Mathematical Physics, Vol. 65, No. 2, 28.03.2025, p. 383-402.

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

BibTeX

@article{cad0ff5318ac474783db3b5389a4345a,

title = "Numerical Analysis of Stability Loss for Poiseuille-Type Polymer Fluid Flows under the Pulsed Effect of Pressure and Temperature",

abstract = "Abstract: A system of nonstationary partial differential equations is obtained, describing non-isothermal Poiseuille-type flows of an incompressible viscoelastic polymer fluid in a channel with a cross-section between two confocal ellipses. For the system we posed an initial-boundary value problem describing the flow in the nozzle of a 3D printer with a heating element under the pulsed action of the pressure gradient in the nozzle and of the temperature of the element. For the numerical solution of the problem, an algorithm is developed that takes into account the singularities of the sought-for functions and is based on polynomial and rational approximations in spatial variables and on the use of an implicit difference scheme in time. The distributions of the velocity and temperature of the fluid in the channel, as well as the dependences of flow rate and of average temperature on time, are studied. The critical relations between the amplitudes and durations of impulses acting on the fluid, at which the flow loses stability, are calculated.",

keywords = "Poiseuille-type flow, critical relations between parameters, loss of stability, mesoscopic rheological model, polymer fluid, polynomial with Dirichlet kernel, pulsed effect, rational barycentric interpolation",

author = "Semisalov, {B. V.} and Bugoets, {I. A.} and Kutkin, {L. I.} and Shapeev, {V. P.}",

note = "The work of B.V. Semisalov was carried out within the framework of the state contract of the Sobolev Institute of Mathematics SB RAS (project no. FWNF-2022-0008). The work of I.A. Bugoets, L.I. Kutkin, and V.P. Shapeev was supported by the Russian Science Foundation (grant no. 23-21-00499). ",

year = "2025",

month = mar,

day = "28",

doi = "10.1134/S0965542524701975",

language = "English",

volume = "65",

pages = "383--402",

journal = "Computational Mathematics and Mathematical Physics",

issn = "0965-5425",

publisher = "Pleiades Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Numerical Analysis of Stability Loss for Poiseuille-Type Polymer Fluid Flows under the Pulsed Effect of Pressure and Temperature

AU - Semisalov, B. V.

AU - Bugoets, I. A.

AU - Kutkin, L. I.

AU - Shapeev, V. P.

N1 - The work of B.V. Semisalov was carried out within the framework of the state contract of the Sobolev Institute of Mathematics SB RAS (project no. FWNF-2022-0008). The work of I.A. Bugoets, L.I. Kutkin, and V.P. Shapeev was supported by the Russian Science Foundation (grant no. 23-21-00499).

PY - 2025/3/28

Y1 - 2025/3/28

N2 - Abstract: A system of nonstationary partial differential equations is obtained, describing non-isothermal Poiseuille-type flows of an incompressible viscoelastic polymer fluid in a channel with a cross-section between two confocal ellipses. For the system we posed an initial-boundary value problem describing the flow in the nozzle of a 3D printer with a heating element under the pulsed action of the pressure gradient in the nozzle and of the temperature of the element. For the numerical solution of the problem, an algorithm is developed that takes into account the singularities of the sought-for functions and is based on polynomial and rational approximations in spatial variables and on the use of an implicit difference scheme in time. The distributions of the velocity and temperature of the fluid in the channel, as well as the dependences of flow rate and of average temperature on time, are studied. The critical relations between the amplitudes and durations of impulses acting on the fluid, at which the flow loses stability, are calculated.

AB - Abstract: A system of nonstationary partial differential equations is obtained, describing non-isothermal Poiseuille-type flows of an incompressible viscoelastic polymer fluid in a channel with a cross-section between two confocal ellipses. For the system we posed an initial-boundary value problem describing the flow in the nozzle of a 3D printer with a heating element under the pulsed action of the pressure gradient in the nozzle and of the temperature of the element. For the numerical solution of the problem, an algorithm is developed that takes into account the singularities of the sought-for functions and is based on polynomial and rational approximations in spatial variables and on the use of an implicit difference scheme in time. The distributions of the velocity and temperature of the fluid in the channel, as well as the dependences of flow rate and of average temperature on time, are studied. The critical relations between the amplitudes and durations of impulses acting on the fluid, at which the flow loses stability, are calculated.

KW - Poiseuille-type flow

KW - critical relations between parameters

KW - loss of stability

KW - mesoscopic rheological model

KW - polymer fluid

KW - polynomial with Dirichlet kernel

KW - pulsed effect

KW - rational barycentric interpolation

UR - https://www.mendeley.com/catalogue/6f133f87-0ce2-30d1-a214-2cf36ee88bd3/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105001570737&origin=inward&txGid=a6dac4577d14294c6165dbc411e16984

U2 - 10.1134/S0965542524701975

DO - 10.1134/S0965542524701975

M3 - Article

VL - 65

SP - 383

EP - 402

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 2

ER -

ID: 65167912