Asymptotic numerical method for steady flow of power-law fluids

• A perturbation method is used to compute nonlinear solutions of steady flow of Power-law fluids.
• A perturbation method, Padé approximants, and the finite element method are associated to determine a numerical method.
• A very simple criterion helps determine bifurcation points in the flow (critical Reynolds numbers).
• 2D numerical examples (flow between two rigid walls, flow in a lid driven cavity, flow in a planar sudden expansion) help show the capability and the efficiency of the proposed numerical method.

This work concerns numerical simulations of Power-law fluids. This non-linear problem is solved by using the Asymptotic-Numerical Method (ANM). As this problem is strongly non-linear, we show how the ANM can be used (introduction of new variables, regularization parameter). A numerical method to compute critical Reynolds numbers, bifurcation points, is also proposed. This method makes it possible to determine accurate critical Reynolds without increasing the computational times. Several numerical examples help to demonstrate the efficiency and the reliability of the proposed methods.