Estimate of Iteration Errors in Computational Fluid Dynamics

Abstract

In this work an empirical estimator is used to estimate the iteration error based on the convergence rate of the variable of interest. Problems of heat transfer and of fluid mechanics are solved by the finite-difference and finite-volume methods using various iteration methods. In the initial iterations the accuracy of the empirical estimator is usually low; when the number of iterations is high, round-off errors predominate over iteration errors, but even so, the accuracy is relatively good; and in the interval between these two extremes, the accuracy tends to improve as the number of iterations increases.

Márcio André Martins acknowledges the Brazilian research support agency CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) and the Postgraduate Program for Numerical Methods in Engineering (PPGMNE), of the Federal University of Paraná (UFPR) (Brazil) for support received during the development of this work. Carlos Henrique Marchi is a scholar of CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico)—Brazil. The authors acknowledge The UNIESPAÇO Program of The Brazilian Space Agency (AEB).