Computation of Anisotropic Conduction Using Unstructured Meshes

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Abstract
This paper presents a conservative finite volume scheme for computing conduction heat transfer in materials with anisotropic conductivity. Unstructured solution-adaptive meshes composed of arbitrary convex polyhedra are used. Discrete energy balances are written over these polyhedra. Temperature gradients required for the evaluation of secondary diffusion fluxes are found by linear reconstruction. A fully implicit scheme is used for unsteady problems. The resulting discrete equations are solved using an algebraic multigrid scheme. Schemes for hanging-node and conformal adaption are implemented. Computations are performed using a variety of triangular and quadrilateral meshes. The results are compared to published analytical and numerical solutions and are shown to be satisfactory.