A Finite Volume Scheme for Diffusion Equations on Distorted Quadrilateral Meshes

References

• Aavatsmark , I. 2002 . An introduction to multipoint flux approximations for quadrilateral grids . Comput. Geosci. , 6 : 404 – 432 .
   Google Scholar
• Aavatsmark , I. and Eigestad , G. T. 2006 . Numerical convergence of the MPFA O-method and U-method for general quadrilateral grids . Int. J. Numer. Meth. Fluids , 51 : 939 – 961 .
   Google Scholar
• Aavatsmark , I. , Barkve , T. , B⊘e , Ø. and Mannseth , T. 1998 . Discretization on unstructured grids for inho-mogeneous, anisotropic media. Part I: Derivation of the methods . SIAM J. Sci. Comput , 19 : 1700 – 1716 .
   Web of Science ®Google Scholar
• Aavatsmark , I. , Barkve , T. , B⊘e , Ø. and Mannseth , T. 1998 . Discretization on unstructured grids for in-homogeneous, anisotropic media. Part II: Discussion and numerical results . SIAM J. Sci. Comput , 19 : 1717 – 1736 .
   Google Scholar
• Breil , J. and Maire , P.-H. 2007 . A cell-centered diffusion scheme on two-dimensional unstructured meshes . J. Comput. Phys. , 224 : 785 – 823 .
   Web of Science ®Google Scholar
• Li , D. , Shui , H. and Tang , M. 1980 . On the finite difference scheme of two-dimensional parabolic equation in a non-rectangular mesh . J. Num. Method & Comp. Appl. , 4 : 217 – 224 .
   Google Scholar
• Hermeline , F. 2000 . A finite volume method for the approximation of diffusion operators on distorted meshes . J. Comput. Phys. , 160 : 481 – 499 .
   Web of Science ®Google Scholar
• Huang , W. and Kappen , A. M. 1998 . A study of cell-center finite volume methods for diffusion equations , University of Kansas . Mathematics Research Report, 98–10-01, Lawrence KS66045
   Google Scholar
• Wu , J. , Fu , S. and Shen , L. 2003 . A difference scheme with high resolution for the numerical solution of nonlinear diffusion equation . J. Num. Method & Comp. Appl. , 24 : 116 – 128 .
   Google Scholar
• Kershaw , D. S. 1981 . Differencing of the diffusion equation in Lagrangian hydrodynamic codes . J. Comput. Phys. , 39 : 375 – 395 .
   Web of Science ®Google Scholar
• Klausena , R. A. and Russell , T. F. 2004 . Relationships among some locally conservative discretization methods which handle discontinuous coefficients . Comput. Geosci. , 8 : 341 – 377 .
   Google Scholar
• Lipnikov , K. , Shashkov , M. and Svyatskiy , D. 2006 . The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes . J. Comput. Phys. , 211 : 473 – 491 .
   Web of Science ®Google Scholar
• Morel , J. E. , Dendy , J. E. , Hall , M. L. and White , S. W. 1992 . A cell centered Lagrangian-mesh diffusion differencing scheme . J. Comput. Phys. , 103 : 286 – 299 .
   Web of Science ®Google Scholar
• Morel , J. E. , Roberts , R. M. and Shashkov , M. J. 1998 . A local support-operators diffusion discretization scheme for quadrilateral rz meshes . J. Comput. Phys. , 144 : 17 – 51 .
   Web of Science ®Google Scholar
• Saad , Y. 1996 . Iterative method for sparse linear systems , New York : PWS publishing .
   Google Scholar
• Shashkov , M. and Steinberg , S. 1995 . Support-operator finite-difference algorithms for general elliptic problems . J. Comput. Phys. , 118 : 131
   Web of Science ®Google Scholar
• Shashkov , M. 1996 . Conservarive finite-difference methods on general grids , Boca Raton, FL : CRC Press .
   Google Scholar
• Sheng , Z. and Yuan , G. 2008 . A Nine Point Scheme for the Approximation of Diffusion Operators on Distorted Quadrilateral Meshes. SIAM . J. Sci. Comput. , 30 : 1341 – 1361 .
   Google Scholar
• Yuan , G. and Sheng , Z. 2007 . Analysis of accuracy of a finite volume scheme for diffusion equations on distorted meshes . J. Comput. Phys. , 224 : 1170 – 1189 .
   Web of Science ®Google Scholar