Eigenfunction Expansions for Coupled Nonlinear Convection-Diffusion Problems in Complex Physical Domains

7th European Thermal-Sciences Conference

Cotta, R.M.^1,4 ; Naveira-Cotta, C.P.^1 ; Knupp, D.C.^2 ; Zotin, J.L.Z.^1,3 ; Pontes, P.C.^1

Mechanical Eng. Dept.-COPPE, Federal University of Rio de Janeiro, UFRJ, Brazil^1

Mech. Eng. Dept. - Polytechnic Inst., State Univ. of Rio de Janeiro, UERJ, Brazil^2

Centro Federal de Educacao Tecnológica Celso Suckow da Fonseca, CEFET/RJ, Itaguaí, Brazil^3

National Commission of Nuclear Energy, CNEN, Rio de Janeiro, Brazil^4

关键词: Application examples;    Complex geometries;    Convergence characteristics;    Eigenfunction expansions;    Generalized integral transforms;    Integral transformations;    Nonlinear convection;    Nonlinear eigenvalue problem;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/745/2/022001/pdf
DOI  :  10.1088/1742-6596/745/2/022001

来源: IOP

【 摘 要 】

This lecture offers an updated review on the Generalized Integral Transform Technique (GITT), with focus on handling complex geometries, coupled problems, and nonlinear convection-diffusion, so as to illustrate some new application paradigms. Special emphasis is given to demonstrating novel developments, such as a single domain reformulation strategy that simplifies the treatment of complex geometries, an integral balance scheme in handling multiscale problems, the adoption of convective eigenvalue problems in dealing with strongly convective formulations, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Representative application examples are then provided that employ recent extensions on the Generalized Integral Transform Technique (GITT), and a few numerical results are reported to illustrate the convergence characteristics of the proposed eigenfunction expansions.