A GENERALIZED INTEGRAL TRANSFORMED TECHNIQUE: LITERATURE REVIEW AND COMPARATIVE RESULTS WITH FINITE VOLUME METHOD

• DOI: 10.22533/at.ed.8632026108

• Palavras-chave: Generalized Integral Transform Technique, Diffusion-advection, Convergence Rate, Literature Review

• Keywords: Generalized Integral Transform Technique, Diffusion-advection, Convergence Rate, Literature Review

• Abstract:

  This work aims to carry out a brief review of the literature on the use of the Generalized Integral Transform Technique (GITT) in diffusion-advection problems in engineering and to analyze two works that compare the solution of a problem via GITT and the Finite Element Method (FVM). A bibliographic survey was carried out in the Google Scholar and Science Direct databases, in conference proceedings and periodicals. During the bibliographic survey phase, care was taken to research whether there was any work in the literature like the one proposed in this article, but it was not found. GITT's step by step will be presented, through the mathematical development of an engineering problem present in one of the selected articles. A brief review of the literature on the technique over the past 25 years, with a summary of 24 papers, shows the range of applications of the technique in different areas. After reviewing the literature, comparative results are presented between the solutions via GITT and FVM, two studies analyzed, showing the effectiveness of GITT and a higher rate of convergence. It is concluded that GITT has been shown to be a powerful tool in solving diffusion-advection problems, in addition to providing low computational cost, when compared to FVM.

• Número de páginas: 23