scholarly journals Recent advances in computational-analytical integral transforms for convection-diffusion problems

2017 ◽  
Vol 54 (8) ◽  
pp. 2475-2496 ◽  
Author(s):  
R. M. Cotta ◽  
C. P. Naveira-Cotta ◽  
D. C. Knupp ◽  
J. L. Z. Zotin ◽  
P. C. Pontes ◽  
...  
Keyword(s):  
Integral Transforms ◽  
Convection Diffusion ◽  
Recent Advances ◽  
Diffusion Problems

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

2010 ◽  
Author(s):  
Renato M. Cotta ◽  
Joa˜o N. N. Quaresma ◽  
Leandro A. Sphaier ◽  
Carolina P. Naveira-Cotta
Keyword(s):  
Open Source ◽  
Integral Transform ◽  
Nonlinear Partial Differential Equations ◽  
Integral Transforms ◽  
Analytical Methodology ◽  
Convection Diffusion ◽  
Development Platform ◽  
Unit Code ◽  
Nonlinear Transient ◽  
Diffusion Problems

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 — Unified Integral Transforms, 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.

scholarly journals Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems

2013 ◽  
Vol 63 (11) ◽  
pp. 840-866 ◽  
Author(s):  
Renato M. Cotta ◽  
Diego C. Knupp ◽  
Carolina P. Naveira-Cotta ◽  
Leandro A. Sphaier ◽  
João N. N. Quaresma
Keyword(s):  
Integral Transforms ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Diffusion Problems
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