TITLE:
A Comparison between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations
AUTHORS:
Abdul-Sattar J. Al-Saif, Assma J. Harfash
KEYWORDS:
Unsteady Incompressible Viscous Flows, Reduced Differential Transform Method, Perturbation-Iteration Algorithm
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.12,
December
12,
2018
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.