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Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects pp 293–301Cite as

A Linearity-Preserving Cell-Centered Scheme for the Anisotropic Diffusion Equations

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 77))

Abstract

In this paper a cell-centered discretization scheme for the heterogeneous and anisotropic diffusion problems is proposed on general polygonal meshes. The unknowns are the values at the cell center and the scheme relies on linearity-preserving criterion and the use of the harmonic averaging points located at the interface of heterogeneity. Numerical results show that our scheme is robust, and the optimal convergence rates are verified on general distorted meshes in case that the diffusion tensor is taken to be anisotropic, at times discontinuous.

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References

  1. Agelas, L., Eymard, R., Herbin, R.: A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media. CR Acad. Sci. Paris Ser. I347, 673–676 (2009)

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  4. Wu, J.M., Gao, Z.M., Dai, Z.H.: A stabilized linearity-preserving scheme for the heterogeneous and anisotropic diffusion problems on polygonal meshes. J. Comput. Phys. 231, 7152–7169 (2012)

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Acknowledgments

The authors thank the anonymous reviewers for their useful suggestions. This work is supported by the National Natural Science Fundation of China (Nos. 91330107, 61170309, 11135007) and the Science Foundation of China Academy of Engineering Physics (2013B0202034).

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing, 100088, China

    Zhi-Ming Gao & Ji-Ming Wu

Authors
  1. Zhi-Ming Gao
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  2. Ji-Ming Wu
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Correspondence to Zhi-Ming Gao .

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Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

  2. Institute Comp. Applied Mathematics, University of Münster Center for Nonlinear Sciences (CeNoS ), Münster, Germany

    Mario Ohlberger

  3. Inst. Appl. Analysis and Num. Simulation, University of Stuttgart, Stuttgart, Germany

    Christian Rohde

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Gao, ZM., Wu, JM. (2014). A Linearity-Preserving Cell-Centered Scheme for the Anisotropic Diffusion Equations. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_28

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