In this paper, a high accurate finite volume method is given for diffusion equations with anisotropic diffusion coefficients on unstructured meshes. In order to deal with distorted meshes, the vertex unknowns are introduced as the middle quantities in the construction of this method besides the cell-centered unknowns. The "twin-fitting" method is applied to computing the vertex unknowns for diffusion equations with anisotropic coefficients, so that the resulting method is solved by the cell-centered unknowns. Numerical experiments show that this method can deal with distorted meshes and anisotropic diffusion coefficient problem.
. HIGH ACCURATE COMPUTATION OF DIFFUSION EQUATIONS WITH ANISOTROPIC COEFFICIENTS[J]. Journal of Numerical Methods and Computer Applicat, 2017, 38(4): 312-326.
Aavatsmark I, Barkve T, Bøe Ø, Aannseth T. Discretization on unstructured grids for inhomogeneous, anisotropic media. Part I:Derivation of the methods[J]. SIAM J. Sci. Comput., 1998, 19:1700-1716.
Aavatsmark I, Barkve T, Bøe Ø, Aannseth T. Discretization on unstructured grids for inhomogeneous, anisotropic media. Part II:Discussion and numerical results[J]. SIAM J. Sci. Comput., 1998, 19:1717-1736.
Aavatsmark I. An introduction to multipoint flux approximations for quadrilateral grids[J]. Comput. Geosci., 2002, 6:405-432.