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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 0.7

ISSN Druckformat: 1940-2503
ISSN Online: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2015012337
pages 105-121


Eduardo Divo
Department of Mechanical Engineering, Embry-Riddle Aeronautical University, 600 S Clyde Morris Blvd, Daytona Beach, Florida, USA
Hussein Saad
Department of Mechanical Engineering, Embry-Riddle Aeronautical University, Daytona Beach, Florida, USA; Foundation of Technical Education, Najaf Technical College, Najaf, Iraq
Sandra Boetcher
Embry-Riddle Aeronautical University, Daytona Beach, FL, 32114
Jeff Brown
Department of Civil Engineering Embry-Riddle Aeronautical University, Daytona Beach, FL, USA
Alain J. Kassab
Department of Mechanical and Aerospace Engineering, University of Central Florida, 4000 Central Florida Blvd, Orlando, Florida, USA


A novel computational tool based on the localized radial-basis function (RBF) collocation (LRC) meshless method coupled with a volume-of-fluid (VoF) scheme capable of accurately and efficiently solving transient multidimensional heat conduction problems in composite and heterogeneous media is formulated and implemented. While the LRC meshless method lends its inherent advantages of spectral convergence and ease of automation, the VoF scheme allows one to effectively and efficiently simulate the location, size, and shape of cavities, voids, inclusions, defects, or deattachments in the conducting media without the need to regenerate point distributions, boundaries, or interpolation matrices. To this end, the inverse geometric problem of cavity detection can be formulated as an optimization problem that minimizes an objective function that computes the deviation of measured temperatures at accessible locations to those generated by the LRC-VoF meshless method. The LRC-VoF meshless algorithms will be driven by an optimization code based on the genetic algorithms technique, which can efficiently search for the optimal set of design parameters (location, size, shape, etc.) within a predefined design space. Initial guesses to the search algorithm will be provided by the classical 1D semi-infinite composite analytical solution, which can predict the approximate location of the cavity. The LRC-VoF formulation is tested and validated through a series of controlled numerical experiments. The proposed approach will allow solving the onerous computational inverse geometric problem in a very efficient and robust manner while affording its implementation in modest computational platforms, thereby realizing the disruptive potential of the proposed multidimensional high-fidelity nondestructive evaluation (NDE) method.