An optimal variational iteration method for investigating the physical behavior of quasi-steady squeezing flow confined between parallel rigid walls

Abstract

An efficient numerical method for investigating the physical behavior of an axisymmetric 2D incompressible squeeze flow between two rigid parallel plates is proposed. Due to the low velocity of the moving rigid wall, the flow is considered as a quasi-steady flow. The nonlinear governing equations can be transformed to a single fourth-order nonlinear differential equation. A new efficient iteration method based on coupling of variational iteration method with some auxiliary convergence-control parameters, known as the optimal variational iteration method is proposed to obtain a solution for the generated nonlinear fourth-order differential equation. In the proposed method, the residual function and its error of norm two are implemented to change the problem into an optimization one in order to choose the auxiliary convergence-control parameters optimally. Consequently, a good approximate solution is obtained. The main benefit of the proposed method is the availability of adjusting and controlling the convergence region in an easy way. This property leads to faster convergence, simplicity of wide-range application and efficiency. To show the efficiency and accuracy of the established method, the problem is also solved by various iterative methods, such as perturbation method, homotopy perturbation method and optimal homotopy asymptotic method. As a comparison, the proposed method provides a straightforward way to control the convergence and consequently readily tuning the convergence regions. These properties lead to quick convergence to the exact solution and needing less computational efforts.