A numerical study for multiple solutions of a singular boundary value problem arising from laminar flow in a porous pipe with moving wall

Lin Li, Ping Lin (Lead / Corresponding author), Xinhui Si, Liancun Zheng

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9 Citations (Scopus)
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Abstract

This paper is concerned with multiple solutions of a singular nonlinear boundary value problem (BVP) on the interval [0,1], which arises in a study of the laminar flow in a porous pipe with an expanding or contracting wall. For the singular nonlinear BVP, the correct boundary conditions are derived to guarantee that its linearization has a unique smooth solution. Then a numerical technique is proposed to find all possible multiple solutions. For the suction driven pipe flow with the expanding wall (e.g. α=2), we find a new solution numerically and classify it as a type VI solution. The computed results agree well with what can be obtained by the bifurcation package AUTO. In addition, we also construct asymptotic solutions for a few cases of parameters, which agree well with numerical solutions. These serve as validations of our numerical results. Thus we believe that the numerical technique designed in the paper is reliable, and may be further applied to solve a variety of nonlinear equations that arise from other flow problems.

Original languageEnglish
Pages (from-to)536-549
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume313
Early online date20 Oct 2016
DOIs
Publication statusPublished - 15 Mar 2017

Keywords

  • Expanding porous circular pipe
  • Multiple solutions
  • Singular boundary value problem
  • Singular perturbation method

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