Generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 3 May 2016
Abstract
Purpose
The purpose of this paper is to present outcomes of efforts made over the last 20 years to extend the applicability of the Richardson extrapolation procedure to numerical predictions of multidimensional, steady and unsteady, fluid flow and heat transfer phenomena in regular and irregular calculation domains.
Design/methodology/approach
Pattern-preserving grid-refinement strategies are proposed for mathematically rigorous generalizations of the Richardson extrapolation procedure for numerical predictions of steady fluid flow and heat transfer, using finite volume methods and structured multidimensional Cartesian grids; and control-volume finite element methods and unstructured two-dimensional planar grids, consisting of three-node triangular elements. Mathematically sound extrapolation procedures are also proposed for numerical solutions of unsteady and boundary-layer-type problems. The applicability of such procedures to numerical solutions of problems with curved boundaries and internal interfaces, and also those based on unstructured grids of general quadrilateral, tetrahedral, or hexahedral elements, is discussed.
Findings
Applications to three demonstration problems, with discretizations in the asymptotic regime, showed the following: the apparent orders of accuracy were the same as those of the numerical methods used; and the extrapolated results, measures of error, and a grid convergence index, could be obtained in a smooth and non-oscillatory manner.
Originality/value
Strict or approximate pattern-preserving grid-refinement strategies are used to propose generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions. Such extrapolation procedures play an indispensable role in the verification and validation techniques that are employed to assess the accuracy of numerical predictions which are used for designing, optimizing, virtual prototyping, and certification of thermofluid systems.
Keywords
Acknowledgements
The authors are grateful to the Natural Sciences and Engineering Research Council (NSERC) of Canada for supporting this work through research grants to the first author. Financial support from the Fonds de recherche du Québec nature et technologies (FRQNT), a Graduate Excellence Fellowship, and teaching assistantships provided by the Faculty of Engineering and the Department of Mechanical Engineering at McGill University to the second author are all greatly appreciated. Some of the research contributions of several of the first author ' s former graduate students, in particular, Drs N. Elkouh, S. Sebben, D. Venditti, D. Scott, and A. Lamoureux, have been adapted and used in this paper. Some of the material presented in this paper was used in an invited keynote lecture given by the first author (verbal presentation and a one-paragraph abstract only) at the 6th International Symposium on Advances in Computational Heat Transfer (CHT-15) held at Rutgers University, New Jersey, USA, May 24-29, 2015. The first author would also like to express his gratitude to Professor R.W. Lewis for inviting him to contribute a refereed paper to the 25th anniversary issue of this journal.
Citation
Baliga, B.R.(R). and Lokhmanets, I.Y. (2016), "Generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 3/4, pp. 1121-1144. https://doi.org/10.1108/HFF-10-2015-0445
Publisher
:Emerald Group Publishing Limited
Copyright © 2016, Emerald Group Publishing Limited