TY - JOUR
T1 - A Study of Multiple Solutions for the Navier-Stokes Equations by a Finite Element Method
AU - Huanxia Xu, Ping Lin & Xinhui Si
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 107
EP - 122
PY - 2014
DA - 2014/07
SN - 7
DO - http://doi.org/10.4208/nmtma.2014.1236nm
UR - https://global-sci.org/intro/article_detail/nmtma/5867.html
KW - Finite element method, Navier-Stokes equations, porous channel, expanding walls.
AB - <p style="text-align: justify;">In this paper, a finite element method is proposed to investigate multiple solutions of the Navier-Stokes equations for an unsteady, laminar, incompressible flow in
a porous expanding channel. Dual or triple solutions for the fixed values of the wall suction Reynolds number $R$ and the expansion ratio $α$ are obtained numerically. The computed multiple solutions for the symmetric flow are validated by comparing them with
approximate analytic solutions obtained by the similarity transformation and homotopy analysis method. Unlike previous works, our method deals with the Navier-Stokes
equations directly and thus has no similarity and other restrictions as in previous works.
Finally we use the method to study multiple solutions for three cases of the asymmetric
flow (which has not been studied before using the similarity-type techniques).</p>