Higher-Order Nodal Integral Method for the Numerical Solution of Incompressible Fluid Flow Equations

H. S. Amrani1*, M.Akhmouch2, N.Guessous3

1 Laboratoire d'analyse numérique Dep Math et informatique Faculté des siences Dhar El Mahraz,

BP 1796, ATLAS Fès-Morocco.

2 FST-FES-Saiss, Dept of Mathematics Route Immouzer, BP.2202. Fès, Morocco.

3 ENS-FES, BP.5206 Bensouda. Fès, Morocco.

* Corresponding author. E-mail: souhli_a@yahoo.fr

Received: 27 January 2005; revised version accepted: 15 June 2006

Abstract

The higher order nodal integral methods (HONIM) are developed for steady state incompressible fluid flow problems in rectangular geometry. A sequence of polynomial-weighted transverse integration is used to obtain a system of ordinary differential equations (ODE). The leakage terms arising from the integration are incorporated into the inhomogeneous part of the ODEs which are approximated by a Legendre polynomial finite development. The nonlinearity of the convection terms in the continuous equations is reflected in the derived nonlinear system of discrete equations witch are solved by Newton methods. The HONIM of the first order are implemented and tested for the inlet flow between parallel plates and the modified driven cavity problem

Keywords: Numerical methods; Nodal methods; Fluid flow; Navier-Stokes equations; Higher-order nodal integral method.

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