Homotopy Analysis Method for Solving (2+1)-Dimensional Navier-Stokes Equations with Perturbation Terms

Abstract

In this paper Homotopy Analysis Method (HAM) is implemented for obtaining approximate solutions of (2+1)-dimensional Navier-Stokes equations with perturbation terms. The initial approximations are obtained using linear systems of the Navier-Stokes equations; by the iterations formula of HAM, the first approximation solutions and the second approximation solutions are successively obtained and Homotopy Perturbation Method (HPM) is also used to solve these equations; finally, approximate solutions by HAM of (2+1)-dimensional Navier-Stokes equations without perturbation terms and with perturbation terms are compared. Because of the freedom of choice the auxiliary parameter of HAM, the results demonstrate that the rapid convergence and the high accuracy of the HAM in solving Navier-Stokes equations; due to the effects of perturbation terms, the 3rd-order approximation solutions by HAM and HPM have great fluctuation.