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Monotone Finite Volume Schemes for Diffusion Equation with Imperfect Interface on Distorted Meshes

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Abstract

In this paper, we prove the solution of diffusion equation with imperfect interface is positivity-preserving and a monotone finite volume method is presented to obtain the nonnegative solution on distorted mesh. Motivated by Sheng and Yuan (J Comput Phys 231:3739–3754, 2012), the discrete normal flux on interface is defined by using an extended stencil and introducing two auxiliary points to distinguish the discontinuities of the unknowns on both sides of the interface. The resulting finite volume scheme is locally conservative and has only cell-centered unknowns. Moreover, it is proved to be monotone. The numerical results show that the method obtains second order convergent rate in \(L_2\) norms for solutions on quadrilateral and triangular meshes.

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Authors and Affiliations

  1. School of Science, Inner Mongolia University of Science and Technology, Baotou, 014010, Inner Mongolia, People’s Republic of China

    Fujun Cao

  2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing, 100088, People’s Republic of China

    Zhiqiang Sheng & Guangwei Yuan

Authors
  1. Fujun Cao
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  2. Zhiqiang Sheng
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  3. Guangwei Yuan
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Corresponding author

Correspondence to Guangwei Yuan.

Additional information

This work is partially supported by the National Natural Science Foundation of China (11571048, 11571047, 11671049), NSAF (U1630249), Science Challenge Project (No. JCKY2016212A502), the Foundation of CAEP (2015B0202042) and the Inner Mongolia Autonomous Region University Scientific Research Project (NJZZ18140).

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Cao, F., Sheng, Z. & Yuan, G. Monotone Finite Volume Schemes for Diffusion Equation with Imperfect Interface on Distorted Meshes. J Sci Comput 76, 1055–1077 (2018). https://doi.org/10.1007/s10915-018-0651-8

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  • DOI: https://doi.org/10.1007/s10915-018-0651-8

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