Showing 2 results for AFSHAR M.H.
Afshar M.h.,
Volume 1, Issue 1 (September 2003)
Abstract
In this paper the analysis of the pipe networks is formulated as a nonlinear unconstrained optimization problem and solved by a general purpose optimization tool. The formulation is based on the minimization of the total potential energy of the network with respect to the nodal heads. An analogy with the analysis of the skeletal structures is used to derive tire formulation. The proposed formulation owes its significance for use in pipe network optimization algorithms. The ability and versatility of the method to simulate different pipe networks are numerically tested and the accuracy of the results is compared with direct network algorithms.
Afshar M.h.,
Volume 1, Issue 2 (December 2003)
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.
