%0 Journal Article
%A Kattoura, Simon
%A Lamoureux, Alexandre
%A Baliga, Bantwal Rabi
%D 2013
%I Begell House
%K diffusion-type phenomena, anisotropic media, irregular domains, control-volume finite element method, tetrahedral elements, vertex-centered polyhedral control volumes, element-based interpolation functions, sequential iterative variable adjustment procedure
%N 3
%P 249-260
%R 10.1615/ComputThermalScien.2013006532
%T A CONTROL-VOLUME FINITE ELEMENT METHOD FOR THE PREDICTION OF THREE-DIMENSIONAL DIFFUSION-TYPE PHENOMENA IN ANISOTROPIC MEDIA
%U http://dl.begellhouse.com/journals/648192910890cd0e,2e2d35a1125a6cd1,3a9871e147f9bfe2.html
%V 5
%X 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.
%8 2013-04-23