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An approximated solution to the 2D incompressible Navier-Stokes equations via Adomian Decomposition Method
, Article WSEAS Transactions on Mathematics ; Volume 5, Issue 7 , 2006 , Pages 878-885 ; 11092769 (ISSN) ; Taeibi Rahni, M ; Aavani, K ; Sharif University of Technology
2006
Abstract
The Adomian Decomposition Method (ADM) for solving the highly non-linear vorticity-stream function formulation of 2D incompressible Navier-Stokes equations has been implemented. The analysis is accompanied by numerical boundary conditions. Also, numerical simulation, using finite difference method (FDM), is performed for comparison purposes. The obtained results only for few terms of the expansion are presented. Because present software such as Mathematica/Maple can not calculate many terms (for example: up to 10 terms) of solution and then ADM approach of this problem is an open problem case
Stabilized Meshless Local Petrov-Galerkin (MLPG) method for incompressible viscous fluid flows
, Article CMES - Computer Modeling in Engineering and Sciences ; Volume 29, Issue 2 , 2008 , Pages 75-94 ; 15261492 (ISSN) ; Sharif University of Technology
2008
Abstract
In this paper, the truly Meshless Local Petrov-Galerkin (MLPG) method is extended for computation of steady incompressible flows, governed by the Navier-Stokes equations (NSE), in vorticity-stream function formulation. The present method is a truly meshless method based on only a number of randomly located nodes. The formulation is based on two equations including stream function Poisson equation and vorticity advection-dispersion-reaction equation (ADRE). The meshless method is based on a local weighted residual method with the Heaviside step function and quartic spline as the test functions respectively over a local subdomain. Radial basis functions (RBF) interpolation is employed in shape...