A Second Order Control-Volume Finite-Element Least-Squares Strategy for Simulating Diffusion in Strongly Anisotropic Media
Year: 2005
Journal of Computational Mathematics, Vol. 23 (2005), Iss. 1 : pp. 1–16
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-JCM-8791
Journal of Computational Mathematics, Vol. 23 (2005), Iss. 1 : pp. 1–16
Published online: 2005-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Error correction term Shape functions Gradient reconstruction Flux approximation.