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Unified Integral Transform Approach in the Hybrid Solution of Multidimensional Nonlinear Convection-Diffusion Problems

[+] Author Affiliations
Renato M. Cotta, Carolina P. Naveira-Cotta

Federal University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil

João N. N. Quaresma

Federal University of Pará, Belém, PA, Brazil

Leandro A. Sphaier

Universidade Federal Fluminense, Niterói, RJ, Brazil

Paper No. IHTC14-22396, pp. 477-486; 10 pages
  • 2010 14th International Heat Transfer Conference
  • 2010 14th International Heat Transfer Conference, Volume 2
  • Washington, DC, USA, August 8–13, 2010
  • Conference Sponsors: Heat Transfer Division
  • ISBN: 978-0-7918-4937-8 | eISBN: 978-0-7918-3879-2
  • Copyright © 2010 by ASME


The present work summarizes the theory and describes the algorithm related to the construction of an open source mixed symbolic-numerical computational code named UNIT — Un ified I ntegral T ransforms, that provides a development platform for finding solutions of linear and nonlinear partial differential equations via integral transforms. The reported research was performed by making use of the symbolic computational system Mathematica v.7.0 and the hybrid numerical-analytical methodology Generalized Integral Transform Technique — GITT. The aim here is to illustrate the robust and precision controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source code. Test cases are selected based on nonlinear multi-dimensional formulations of the Burgers equations, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects and computational behaviors of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code.

Copyright © 2010 by ASME



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