Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 696253, 13 pages
Research Article

Improving Accuracy of Coarse Grid Numerical Solution of Solid-Solid Reactions by Taylor Series Expansion of the Reaction Term

Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada

Received 28 November 2008; Accepted 12 February 2009

Academic Editor: J. Jiang

Copyright © 2009 Hassan Hassanzadeh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Exothermic solid-solid reactions lead to sharp reaction fronts that cannot be captured by coarse spatial mesh size numerical simulations that are often required for large-scale simulations. We present a coarse-scale formulation with high accuracy by using a Taylor series expansion of the reaction term. Results show that such expansion could adequately maintain the accuracy of fine-scale behavior of a constant pattern reaction front while using a smaller number of numerical grid cells. Results for a one-dimensional solid-solid reacting system reveal reasonable computational time saving. The presented formulation improves our capabilities for conducting fast and accurate numerical simulations of industrial-scale solid-solid reactions.