Abo Bibliothek: Guest
Digitales Portal Digitale Bibliothek eBooks Zeitschriften Referenzen und Berichte Forschungssammlungen
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.2013006532
pages 249-260

A CONTROL-VOLUME FINITE ELEMENT METHOD FOR THE PREDICTION OF THREE-DIMENSIONAL DIFFUSION-TYPE PHENOMENA IN ANISOTROPIC MEDIA

Simon Kattoura
Heat Transfer Laboratory, Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 0C3, Canada
Alexandre Lamoureux
Heat Transfer Laboratory, Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 0C3, Canada
Bantwal Rabi Baliga
Heat Transfer Laboratory, Department of Mechanical Engineering, McGill University, 817 Sherbrooke St. W., Montreal, QC H3A 2K6, Canada

ABSTRAKT

The formulation and testing of a control-volume finite element method (CVFEM) for the prediction of 3D, linear and nonlinear, diffusion-type phenomena in anisotropic media in irregular calculation domains are presented. The calculation domain is discretized into four-node tetrahedral elements. Contiguous, nonoverlapping, polyhedral control volumes are then associated with each node, and the governing differential equation is integrated over these control volumes. In each tetrahedral element, the dependent variable is interpolated linearly, centroidal values of the diffusion coefficients are assumed to prevail, and nodal values of the coefficients in the linearized source term are assumed to prevail over the polyhedral sub–control volumes. These interpolation functions are used to derive the discretized equations, which, in general, are nonlinear and coupled, and are solved using an iterative procedure. Comments are provided on the sufficient conditions for ensuring positive coefficients in the discretized equations. The proposed CVFEM appears to be the first numerical method for the solution of anisotropic diffusion-type problems that is based on tetrahedral elements and vertex-centered polyhedral control volumes. These features make it particularly attractive for amalgamation with adaptive-grid schemes and applications to problems with complex irregular geometries. The proposed 3D CVFEM and its computer implementation were tested using several steady conduction–type problems, for which analytical solutions were constructed using a special technique. In all cases, the agreement between the numerical and analytical solutions was excellent.


Articles with similar content:

Numerical Simulation of Natural Convection in a Vertical Channel with irregular walls
ICHMT DIGITAL LIBRARY ONLINE, Vol.0, 2015, issue
Abdellah Bekacem, Noureddine Kaid, Mohammed Hasnat, Belkacem Draoui, Kouari Mustapha
AN ALGORITHM FOR ANALYZING PLANAR JUNCTIONS OF WAVEGUIDES OF ARBITRARY CROSS-SECTION WITH THE USE OF EIGENFUNCTIONS OF THE COMMON APERTURE
Telecommunications and Radio Engineering, Vol.73, 2014, issue 10
S. O. Steshenko
On the Pontryagin Lower Alternating Integral
Journal of Automation and Information Sciences, Vol.45, 2013, issue 2
Ikrom M. Iskanadjiev
DISCRETE ORDINATES SOLUTION OF RADIATIVE TRANSFER ACROSS A SLAB WITH VARIABLE REFRACTIVE INDEX
ICHMT DIGITAL LIBRARY ONLINE, Vol.15, 2001, issue
Philippe Ben Abdallah
TURBULENT FLOW STRUCTURE IN A CLOSELY-SPACED TRIANGULAR-ARRAY ROD BUNDLE
International Heat Transfer Conference 8, Vol.3, 1986, issue
J. T. Rogers, A. E. E. Tahir