Renato M. Cotta | Diego C. Knupp | Leandro A. Sphaier | Carolina P. Naveira-Cotta | João
N.N. Quaresma
Universidade Federal do Rio de Janeiro, BRAZIL
Abstract: This lecture summarizes the theory and describes the algorithm related to the construction of an open-source mixed symbolical-numerical computational code named UNIT (UNified Integral Transforms) that provides a computational environment for finding solutions of linear and nonlinear partial differential systems via integral transforms. The reported research was performed by employing the well-established analytical-numerical methodology known as the Generalized Integral Transform Technique (GITT), together with symbolic computation provided by the Mathematica system (version 7.0). The main purpose of this presentation is to illustrate the robust precision controlled simulation of multidimensional nonlinear transient convection- diffusion problems, while providing a brief introduction of this open source implementation. Test cases are selected based on nonlinear multi-dimensional formulations of Burgers' equation, with the establishment of reference results for specific numerical values of governing parameters. Special aspects and the computational behavior of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code. Then, the algorithm is illustrated in the solution of various heat and mass transfer problems.