WIAS Preprint No. 1033, (2005)

Numerical simulation of heat transfer in materials with anisotropic thermal conductivity: A finite volume scheme to handle complex geometries


  • Geiser, Juergen
  • Klein, Olaf
    ORCID: 0000-0002-4142-3603
  • Philip, Peter

2010 Mathematics Subject Classification

  • 80A20 80M25 74S10 76R50 35J60 35J65 65M99 65Z05

2008 Physics and Astronomy Classification Scheme

  • 02.60.Cb 44.05.+e 47.27.Te


  • Numerical simulation, Heat transfer. Anisotropic diffusion, Anisotropic thermal conductivity, Finite volume method, Delaunay triangulation, Nonlinear elliptic PDE's


We devise a finite volume scheme for nonlinear heat transfer in materials with anisotropic thermal conductivity. We focus on the difficulties arising from the discretization of complex domains which are typical in the simulation of industrially relevant processes. For polyhedral domains in two dimensions, we consider Cartesian as well as cylindrical coordinates. Our finite volume scheme is based on unstructured constrained Delaunay triangulations of the domain. For simplicity, we assume that the thermal conductivity tensor has vanishing off-diagonal entries and that the anisotropy is independent of the temperature. We present numerical simulations, verifying our finite volume scheme in cases where a closed-form solution is available. Further results demonstrate the effectiveness of the method in computing the heat transfer in a complex growth apparatus used in crystal growth.

Appeared in

  • Adv. Math. Sci. Appl., 18 (2008) pp. 43--67.

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