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Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems pp 723–730Cite as

Piecewise Linear Transformation in Diffusive Flux Discretizations

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 78))

Abstract

A piecewise linear transformation that allows interpolation of diffused concentration over material discontinuities is presented. It may be used either to evaluate concentration values at auxiliary points, or to approximate face fluxes directly. It does not violate the discrete minimum and maximum principles, so it can be used to construct discretization schemes that preserve solution positivity or discrete minimum and maximum principles. The method has been demonstrated to produce second-order accurate interpolated concentration values and first-order accurate fluxes even when interpolation nodes lie at opposite sides of a discontinuity.

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Acknowledgments

The authors wish to thank the Ministry of Education, Science and Technological Development of the Republic of Serbia for financial support through the Technology Development Project TR37014.

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Authors and Affiliations

  1. Jaroslav Černi Institute, Belgrade, Serbia

    D. Vidović, M. Dotlić, B. Pokorni & M. Dimkić

  2. Faculty of Mining and Geology, University of Belgrade, Belgrade, Serbia

    M. Pušić

Authors
  1. D. Vidović
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  2. M. Dotlić
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  3. B. Pokorni
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  4. M. Pušić
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  5. M. Dimkić
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Corresponding author

Correspondence to D. Vidović .

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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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Vidović, D., Dotlić, M., Pokorni, B., Pušić, M., Dimkić, M. (2014). Piecewise Linear Transformation in Diffusive Flux Discretizations. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Springer Proceedings in Mathematics & Statistics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-05591-6_72

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