Paper Information

Journal:   INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING AND PRODUCTION MANAGEMENT (IJIE) (INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE) (PERSIAN)   SUMMER 2007 , Volume 18 , Number 2; Page(s) 1 To 9.
 
Paper: 

MESH LESS DISCRETE LEAST SQUARE METHOD FOR CONVECTION-DIFFUSION PROBLEMS

 
 
Author(s):  ARZANI HAMED, AFSHAR M.H., NAJMAEI M.
 
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Abstract: 
Many meshless methods are presented in recent years for solving partical differential equations. All of them use a background mesh to introducing the Guossian points for solution of the integral equation. Numerical integration has significant effects on convergence and accuracy of solution from many meshless methods. They are meshless only from the point of view of interpolation of the field variables. In this paper we present a fully meshless procedure for linear and nonlinear convection-diffusion equation problems in steady and transient forms. In this new method a fully Least squares method is used in both function approximation and the discretization of the governing differential equations. The discritized equations are obtained via a discrete least squares method in which the sum of the squared residuals are minimized with respect to unknown nodal parameters in the inner and boundary nodes. In this process no numerical integration is needed and the obtained equations are symmetric and positive definite. The shape functions are derived using the moving least squares (MLS) method of function approximation with a spline weighting function. The convergency and accuracy of the method is programmed using visual Fortran 6.5and accuracy of the results are compared and verified with reference to some examples.
 
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