A Comparison between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations

Abdul-Sattar J Al-Saif,Assma J Harfash

doi:10.4236/jamp.2018.612211

Abstract

In this work, approximate analytical solutions to the lid-driven square cavity flow problem, which satisfied two-dimensional unsteady incompressible Navier-Stokes equations, are presented using the kinetically reduced local Navier-Stokes equations. Reduced differential transform method and perturbation-iteration algorithm are applied to solve this problem. The convergence analysis was discussed for both methods. The numerical results of both methods are given at some Reynolds numbers and low Mach numbers, and compared with results of earlier studies in the review of the literatures. These two methods are easy and fast to implement, and the results are close to each other and other numerical results, so it can be said that these methods are useful in finding approximate analytical solutions to the unsteady incompressible flow problems at low Mach numbers.

Highlights

Fluid flow is one of the most important engineering phenomena that have received widespread attention in theoretical and practical scientific research
These two methods are easy and fast to implement, and the results are close to each other and other numerical results, so it can be said that these methods are useful in finding approximate analytical solutions to the unsteady incompressible flow problems at low Mach numbers
We present the approximate analytical solutions for two-dimensional lid-driven cavity flow, which are obtained by applying differential transform method and perturbation-iteration algorithm (Section 5)

Summary

Introduction

Fluid flow is one of the most important engineering phenomena that have received widespread attention in theoretical and practical scientific research. Many of these studies focus on simulated mathematical models which represent these phenomena. The equations of Navier-Stokes, which are the basic. J. Harfash model for describing the movement of fluid, have received considerable attention from researchers to find their analytical and numerical solutions

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