Ertürk, ErcanAllahviranloo, Tofigh2022-12-122022-12-122022Erturk, E., & Allahviranloo, T. (2022). Bifurcation and Multiplicity of Solutions of the Navier–Stokes Equations in Driven Semi-Elliptical Cavity Flow. Mathematics, 10(22), 4242.2227-7390http://dx.doi.org/10.3390/math10224242https://hdl.handle.net/20.500.12713/3465In 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.eninfo:eu-repo/semantics/openAccessNavier-Stokes EquationsSemi-Elliptical Cavity FlowBifurcation Reynolds NumberMultiplicity Of SolutionsArticle1022WOS:0008881229000012-s2.0-85142524373Q110.3390/math10224242Q2