A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

Abstract

An unstructured mesh �nite volume discretisation method for simulating di�usion in
anisotropic media in two-dimensional space is discussed. This technique is considered as an
extension of the fully implicit hybrid control-volume �nite-element method and it retains
the local continuity of the
ux at the control volume faces. A least squares function recon-
struction technique together with a new
ux decomposition strategy is used to obtain an
accurate
ux 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 signi�cantly 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.