Bifurcation and Multiplicity of Solutions of the Navier–Stokes Equations in Driven Semi-Elliptical Cavity Flow

Ercan Erturk () and Tofigh Allahviranloo ()
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Ercan Erturk: Mechanical Engineering Department, Istanbul Medeniyet University, Istanbul 34700, Turkey
Tofigh Allahviranloo: Software Engineering Department, Istinye University, Istanbul 34010, Turkey

Mathematics, 2022, vol. 10, issue 22, 1-20

Abstract: In this paper, bifurcations in the solution of the Navier–Stokes equations are studied and multiple solutions of the driven semi-elliptical cavity flow are presented. The two-dimensional steady incompressible driven viscous flow in a semi-elliptical cavity is solved numerically. To this end, the problem is formulated using an elliptic coordinate system that transforms the geometry conformally and provides a body fitted coordinate system. The presented results show that above a bifurcation Reynolds number the solution of the governing flow equations bifurcates and there exist multiple solutions for a particular Reynolds number when the aspect ratio of the semi-elliptical cavity geometry is 0.26 ⩽ D ⩽ 0.8. The bifurcation Reynolds numbers for different aspect ratios and also multiple solutions at different Reynolds numbers are presented in detail.

Keywords: Navier–Stokes equations; semi-elliptical cavity flow; bifurcation Reynolds number; multiplicity of solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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