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Nonlinear Monotone FV Schemes for Radionuclide Geomigration and Multiphase Flow Models

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Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems

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

Abstract

We present applications of the nonlinear monotone finite volume method to radionuclide transport and multiphase flow in geological media models. The scheme is applicable for full anisotropic discontinuous permeability or diffusion tensors and arbitrary conformal polyhedral cells. We consider two versions of the nonlinear scheme: two-point flux approximation preserving positivity of the solution and compact multi-point flux approximation that provides discrete maximum principle. We compare the new nonlinear schemes with the conventional linear two-point and multi-point (O-scheme) flux approximations. Both new nonlinear schemes have compact stencils and a number of important advantages over the traditional linear discretizations. Two industrial applications are discussed briefly: radionuclides transport modeling within the radioactive waste safety assessment and multiphase flow modeling of oil recovery process.

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Acknowledgments

This work has been supported in part by RFBR grants 12-01-33084, 14-01-00830, Russian Presidential grant MK-7159.2013.1, Federal target programs of Russian Ministry of Education and Science, ExxonMobil Upstream Research Company, and project “Breakthrough” of Rosatom.

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Authors and Affiliations

  1. Institute of Numerical Mathematics, Gubkina 8, Moscow, Russia

    Ivan Kapyrin, Kirill Nikitin, Kirill Terekhov & Yuri Vassilevski

  2. Institute of Nuclear Safety, B. Tulskaya 52, Moscow, Russia

    Ivan Kapyrin & Kirill Nikitin

  3. Moscow Institute of Physics and Technology, Institutski 9, Dolgoprudny, M.R., Russia

    Yuri Vassilevski

Authors
  1. Ivan Kapyrin
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  2. Kirill Nikitin
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  3. Kirill Terekhov
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  4. Yuri Vassilevski
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Corresponding author

Correspondence to Kirill Nikitin .

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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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Kapyrin, I., Nikitin, K., Terekhov, K., Vassilevski, Y. (2014). Nonlinear Monotone FV Schemes for Radionuclide Geomigration and Multiphase Flow Models. 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_65

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