multiplicity of steady state solutions in 2-d incompressible viscous wall driven arc-shaped cavity ‎flow

Numerical simulations of the steady 2-d incompressible viscous flow in an arc-shaped cavity are presented. the navier–stokes equations in streamfunction and vorticity formulation are solved numerically using a body fitted mesh obtained by a conformal mapping. our numerical results reveal that the arc-shaped cavity flow has multiple steady solutions above a bifurcation reynolds number when the arc length ratio is less than 1/2 ( r <1/2). multiple steady state solutions of the arc-shaped cavity flow with different arc length ratios ( r =2/5, 1/3, 1/4, 1/5 and 1/6) are presented at a variety of reynolds numbers. our results show that the bifurcation reynolds number at which a second solution starts to exist changes as the arc length ratio of the arc-shaped cavity changes. among the considered different arc length ratios ( r =2/5, 1/3, 1/4, 1/5 and 1/6), the minimum bifurcation reynolds number occurs at 1/3 arc length ratio with re =5164. detailed results are presented.