Abo Bibliothek: Guest
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 subâ€“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 conductionâ€“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.

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