Analytical approximate solutions for two-dimensional incompressible Navier-Stokes equations

Abstract

Analytical approximate solutions of the two-dimensional incompressible Navier-Stokes equations by means of Adomian decomposition method are presented. The power of this manageable method is confirmed by applying it for two selected  flow problems: The first is the Taylor decaying vortices, and the second is the flow behind a grid, comparison with High-order upwind compact finite-difference method is made. The numerical results that are obtained for two incompressible flow problems  showed that the proposed method is less time consuming, quite accurate and easily implemented. In addition, we prove the convergence of this method when it is applied to the flow problems, which are describing them by  unsteady two-dimensional incompressible Navier-Stokes equations.

Keywords: Navier-Stokes equations, Adomian decomposition, upwind compact difference, Accuracy, Convergence analysis,Taylor's decay vortices, flow behind a grid.