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

An unifying overview of the Generalized Integral Transform Technique (GITT) as a computational-analytical approach for solving convection-diffusion problems is presented. This work is aimed at bringing together some of the most recent developments on both accuracy and convergence improvements on thi...

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Bibliographic Details
Published in:Heat and mass transfer 2018-08, Vol.54 (8), p.2475-2496
Main Authors: Cotta, R. M., Naveira-Cotta, C. P., Knupp, D. C., Zotin, J. L. Z., Pontes, P. C., Almeida, A. P.
Format: Article
Language:English
Subjects:
Accuracy
Burgers equation
Computation
Convection-diffusion equation
Convergence
Diffusion
Eigenvalues
Eigenvectors
Engineering
Engineering Thermodynamics
Formulations
Heat and Mass Transfer
Hollow fiber membranes
Industrial Chemistry/Chemical Engineering
Integral transforms
Mathematical analysis
Mathematical models
Microchannels
Original
Partial differential equations
Substrates
Thermodynamics
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Summary:An unifying overview of the Generalized Integral Transform Technique (GITT) as a computational-analytical approach for solving convection-diffusion problems is presented. This work is aimed at bringing together some of the most recent developments on both accuracy and convergence improvements on this well-established hybrid numerical-analytical methodology for partial differential equations. Special emphasis is given to novel algorithm implementations, all directly connected to enhancing the eigenfunction expansion basis, such as a single domain reformulation strategy for handling complex geometries, an integral balance scheme in dealing with multiscale problems, the adoption of convective eigenvalue problems in formulations with significant convection effects, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Then, selected examples are presented that illustrate the improvement achieved in each class of extension, in terms of convergence acceleration and accuracy gain, which are related to conjugated heat transfer in complex or multiscale microchannel-substrate geometries, multidimensional Burgers equation model, and diffusive metal extraction through polymeric hollow fiber membranes. Numerical results are reported for each application and, where appropriate, critically compared against the traditional GITT scheme without convergence enhancement schemes and commercial or dedicated purely numerical approaches.
ISSN:0947-7411
1432-1181
DOI:10.1007/s00231-017-2186-1