A Study of Multiple Solutions for the Navier-Stokes Equations by a Finite Element Method. Issue 1 (February 2014)

• Record Type: Journal Article
• Authors: Xu, Huanxia; Lin, Ping; Si, Xinhui
• Is Part Of: Numerical mathematics. Volume 7:Issue 1(2014)
• Page Start: 107
• Page End: 122
• Publication Date: 2014-02
• Subjects: 76M10, -- 76D05, -- 74H15; Finite element method, -- Navier-Stokes equations, -- porous channel, -- expanding walls; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.1017/S1004897900000301
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: 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).