Accuracy and convergence of element‐by‐element iterative solvers for incompressible fluid flows using penalty finite element model

Abstract

AbstractThe 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 flow of an incompressible fluid inside a sudden expansion channel is analysed using three meshes of 400, 1600 and 6400 bilinear elements. The iterative 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 influence the choice of the convergence tolerance limit needed to obtain accurate results. An empirical relationship between the element size, the penalty parameter, and the convergence tolerance is presented. This relationship can be used to predict the proper choice of the convergence tolerance for a given penalty parameter and element size.