Abstract

P.A.Jayantha and I.W.Turner
j.pasdunkoralea@student.qut.edu.au, i.turner@fsc.qut.edu.au
School of Mathematical Sciences
Queensland University of Technology
Brisbane, Australia

In this work two different finite volume computational strategies for solving a representative two-dimensional diffusion equation in an orthotropic medium are considered. When the diffusivity tensor is treated as linear, this problem admits an analytical solution that can be used for analysing the accuracy of the proposed numerical methods. In the first method, the gradient approximation techniques discussed in [1] are applied directly to the diffusion equation. In the second method, the diffusion equation is transformed via scaling parameters to an isotropic model and then the control volume techniques discussed in [1] are used to obtain the numerical results on the transformed domain. It is shown that both methods produce reasonable results in comparison with the exact solution for a range of anisotropy ratios typical of wood. However, only the first method is appropriate for use in non-linear coupled transport systems. In summary, the work highlights the necessity of determining a higher order gradient approximation to improve the numerical results on the untransformed domain.

[1] P.A.Jayantha and I.W.Turner, (to appear) A Comparison of Gradient Approximations for use in Finite Volume Computational Models for Two-Dimensional Diffusion Equations, Numerical Heat Transfer, Part B: Fundamentals.

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