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Abstract <p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • B. V. Semisalov,
  • I. A. Bugoets,
  • L. I. Kutkin,
  • V. P. Shapeev

摘要

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.