Paper Information

Journal:   INTERNATIONAL JOURNAL OF CIVIL ENGINEERING   December 2003 , Volume 1 , Number 2; Page(s) 92 To 99.
 
Paper: 

LINEAR AND QUADRATIC LEAST SQUARES FINITE ELEMENT METHOD FOR INCOMPRESSIBLE FLUID FLOW

 
 
Author(s):  AFSHAR M.H.*
 
* 
 
Abstract: 
A least squares finite element method for the .solution of steady incompressible Navier Stokes equations is presented. The Navier-.Stocks equation is first recast into a system of first order partial differential equations with the velocitv. pressure and the vorticity as the main variables. Finite element discretization of the domain introduces a residual in the governing equation which is subsequently minimized in a least squares sense. The method so developed clearly. falls into the minimization category card hence circumventing the L.B.B. condition. Furthermore. the method produces symmetric positive definite matrices which makes the way for using more efficient iterative sobers. A Conjugate Gradient algorithm is, therefore, used for the solution of the resulting .system of linear algebraic equations. To improve the efficiency , of this iterative solver an incomplete Cholesky factorization of the stiffness matrix is used as ct pre-conditioner. Since the storage requirement of the Cholesky factor depends on the bandwidth of matrix. an effective algorithm for the reduction of this bandwidth has also been employed. The application of the method to solve cavity problem and .step flow with different Remolds number is presented to show the applicability of the method to solve practical flows of incompressible fluid The use of both linear and quadratic elements with selective reduced integration is also investigated and the results are presented.
 
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