(untitled) (Journal of Computational Mathematics, 2018)
An unstructured mesh finite volume discretisation method for simulating diffusion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume finite-element method and it retains the local continuity of the flux at the control volume faces. A least squares function reconstruction technique together with a new flux decomposition strategy is used to obtain an accurate flux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it significantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.