Temporal stability analysis for multiple similarity solutions of viscous incompressible flows in porous channels with moving walls

Yanxiao Sun, Ping Lin (Lead / Corresponding author), Lin Li

Research output: Contribution to journalArticle

Abstract

In this paper, a viscous, incompressible laminar fluid flow along a uniformly porous channel with expanding or contracting walls is considered. We present multiple symmetric steady-state solutions of this flow problem at several different expanding ratios, and use the linear stability theory to analyse the temporal stability for these solutions under symmetric, antisymmetric and general perturbations. We construct second order finite difference schemes for the eigenvalue problems with boundary conditions associated with those perturbations, and observe that most of these solutions which are stable under symmetric perturbations are unstable under antisymmetric perturbations. Furthermore, we verify the linear stability analysis results by directly solving the original perturbed nonlinear time dependent problem, and find that both stability results are consistent.

Original languageEnglish
Pages (from-to)738-755
Number of pages18
JournalApplied Mathematical Modelling
Volume77
Issue numberPart 1
Early online date9 Aug 2019
DOIs
Publication statusPublished - Jan 2020

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Incompressible Viscous Flow
Similarity Solution
Incompressible flow
Stability Analysis
Perturbation
Antisymmetric
Linear stability analysis
Flow of fluids
Linear Stability Analysis
Stability Theory
Linear Stability
Steady-state Solution
Laminar Flow
Finite Difference Scheme
Boundary conditions
Eigenvalue Problem
Fluid Flow
Unstable
Verify

Keywords

  • Expansion ratio
  • Laminar flow
  • Moving walls
  • Multiple solutions
  • Temporal stability

Cite this

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title = "Temporal stability analysis for multiple similarity solutions of viscous incompressible flows in porous channels with moving walls",
abstract = "In this paper, a viscous, incompressible laminar fluid flow along a uniformly porous channel with expanding or contracting walls is considered. We present multiple symmetric steady-state solutions of this flow problem at several different expanding ratios, and use the linear stability theory to analyse the temporal stability for these solutions under symmetric, antisymmetric and general perturbations. We construct second order finite difference schemes for the eigenvalue problems with boundary conditions associated with those perturbations, and observe that most of these solutions which are stable under symmetric perturbations are unstable under antisymmetric perturbations. Furthermore, we verify the linear stability analysis results by directly solving the original perturbed nonlinear time dependent problem, and find that both stability results are consistent.",
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AU - Lin, Ping

AU - Li, Lin

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N2 - In this paper, a viscous, incompressible laminar fluid flow along a uniformly porous channel with expanding or contracting walls is considered. We present multiple symmetric steady-state solutions of this flow problem at several different expanding ratios, and use the linear stability theory to analyse the temporal stability for these solutions under symmetric, antisymmetric and general perturbations. We construct second order finite difference schemes for the eigenvalue problems with boundary conditions associated with those perturbations, and observe that most of these solutions which are stable under symmetric perturbations are unstable under antisymmetric perturbations. Furthermore, we verify the linear stability analysis results by directly solving the original perturbed nonlinear time dependent problem, and find that both stability results are consistent.

AB - In this paper, a viscous, incompressible laminar fluid flow along a uniformly porous channel with expanding or contracting walls is considered. We present multiple symmetric steady-state solutions of this flow problem at several different expanding ratios, and use the linear stability theory to analyse the temporal stability for these solutions under symmetric, antisymmetric and general perturbations. We construct second order finite difference schemes for the eigenvalue problems with boundary conditions associated with those perturbations, and observe that most of these solutions which are stable under symmetric perturbations are unstable under antisymmetric perturbations. Furthermore, we verify the linear stability analysis results by directly solving the original perturbed nonlinear time dependent problem, and find that both stability results are consistent.

KW - Expansion ratio

KW - Laminar flow

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KW - Multiple solutions

KW - Temporal stability

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