Finding Steady Poiseuille-Type Flows for Incompressible Polymeric Fluids by the Relaxation Method

A. M. Blokhin, B. V. Semisalov

Research output: Contribution to journalArticlepeer-review

Abstract

Stabilization of flows of an incompressible viscoelastic polymeric fluid in a channel with a rectangular cross section under the action of a constant pressure drop is analyzed numerically. The flows are described within the Pokrovskii–Vinogradov rheological mesoscopic model. An algorithm for solving initial-boundary value problems for nonstationary equations of the model is developed. It uses spatial interpolations with Chebyshev nodes and implicit time integration scheme. It is shown analytically that, in the steady state, the model admits three highly smooth solutions. The question of which of these solutions is realized in practice is investigated by calculating the limit of the solutions of nonstationary equations. It is found that this limit coincides, with high accuracy, with one of the three solutions of the steady-state problem, and the values of parameters at which the switching from one of these solutions to another occurs are calculated.

Original languageEnglish
Pages (from-to)302-315
Number of pages14
JournalComputational Mathematics and Mathematical Physics
Volume62
Issue number2
DOIs
Publication statusPublished - Feb 2022

Keywords

  • mesoscopic rheological model
  • method without saturation
  • polymeric fluid
  • steady Poiseuille flow
  • switching of stabilized solution

OECD FOS+WOS

  • 1.01 MATHEMATICS
  • 1.03 PHYSICAL SCIENCES AND ASTRONOMY

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