Optimum decomposition of the anisotropic diffusion term

A new decomposition method for the discretization of anisotropic diffusion term is developed. The method is a generalization of the optimum decomposition practice adopted in discretizing the isotropic diffusion flux. The new approach is applied in conjunction with the well-known semi-implicit and recently developed modified implicit nonlinear diffusion schemes and used for discretizing the anisotropic diffusion term. The resulting discretization methods are used for solving several anisotropic diffusion problems to compare the performance of the new decomposition technique with the standard one. Results generated demonstrate the virtues of the new method, which leads to a reduction in the CPU times needed for convergence by percentages reaching a level as high as 70%.