Bifurcation Analysis of Incompressible Fluid Flow by a High Order Mesh-Free Indicator with Padé Approximants

In this work, a mesh-free indicator is proposed to detect the bifurcation points of incompressible viscous fluid flow in a 2D sudden expansion. This indicator is mainly based on the high order mesh-free algorithm (HO-MFA) to solve the nonlinear problems obtained from the linear stability analysis. The Padé approximants are then used to improve the validity range of the HO-MFA and to determinate the roots of the indicator. The combination of these mathematical tools allows us to determine the zero of the indicator corresponding to the critical point. The Lyapunov-Schmidt reduction is used to search all the bifurcated branches from the critical point. To show the accuracy of our model, comparisons of the obtained results with those of the literature are made.