年間 6 号発行
ISSN 印刷: 1940-2503
ISSN オンライン: 1940-2554
Indexed in
A CONTROL-VOLUME FINITE ELEMENT METHOD FOR THE PREDICTION OF THREE-DIMENSIONAL DIFFUSION-TYPE PHENOMENA IN ANISOTROPIC MEDIA
要約
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.
-
Baliga Bantwal R., Lokhmanets Iurii, Cimmino Massimo, Numerical Methods for Conduction-Type Phenomena, in Handbook of Thermal Science and Engineering, 2017. Crossref
-
Baliga Bantwal R., Lokhmanets Iurii, Cimmino Massimo, Numerical Methods for Conduction-Type Phenomena, in Handbook of Thermal Science and Engineering, 2018. Crossref
-
Reddy J. N., Kim Namhee, Martinez Matthew, A dual mesh control domain method for the solution of nonlinear Poisson’s equation and the Navier–Stokes equations for incompressible fluids, Physics of Fluids, 32, 9, 2020. Crossref
-
Reddy J.N., Martinez Matthew, Nampally Praneeth, A novel numerical method for the solution of nonlinear equations with applications to heat transfer, International Journal of Numerical Methods for Heat & Fluid Flow, 31, 6, 2021. Crossref