ACCURACY AND CONVERGENCE OF ELEMENT-BY-ELEMENT ITERATIVE SOLVERS FOR INCOMPRESSIBLE FLUID-FLOWS USING PENALTY FINITE-ELEMENT MODEL

The ability of two types of Conjugate Gradient like iterative solvers (GMRES and ORTHOMIN) to resolve large-scale phenomena as a function of mesh density and convergence tolerance limit is investigated. The flo w of an incompressible fluid inside a sudden expansion channel is anal ysed using three meshes of 400, 1600 and 6400 bilinear elements. The i terative solvers utilize the element-by-element data structure of the finite element technique to store and maintain the data at the element level. Both the mesh density and the penalty parameter are found to i nfluence the choice of the convergence tolerance limit needed to obtai n accurate results. An empirical relationship between the element size , the penalty parameter, and the convergence tolerance is presented. T his relationship can be used to predict the proper choice of the conve rgence tolerance for a given penalty parameter and element size.