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Construction of Higher-Order Approximation Difference Scheme for Nonlinear Convection-Diffusion Equation Using Adaptive Artificial Viscosity in Case of Two-Phase Filtering Problems

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Finite Difference Methods. Theory and Applications (FDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

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Abstract

The method of adaptive artificial viscosity is used to model the process of one-dimensional nonlinear convection-diffusion equation. For this purpose, a finite difference scheme (FDS) of the second order of time and space approximation has been developed. The scheme was tested using a numerical solution of the problem on formation of a gradient catastrophe. The process of two-phase filtration was analyzed with the help of constructed FDS. Numerical calculations showed that the proposed method, and in this case reliably tracks the discontinuities of the solution.

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References

  1. Sivukhin, D.V.: General Course of Physics, vol. 2. Nauka, Moscow (1979)

    Google Scholar 

  2. Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Applied Science Publishers Ltd., London (1979)

    Google Scholar 

  3. Koldoba, A.B., Poveschenko, Y.A., Samarskaya, E.A., Tishkin, V.F.: Methods of mathematical modeling of the environment. Nauka, Moscow (2000)

    Google Scholar 

  4. Popov, I.V.: Construction of difference scheme with high order approximation using adaptive artificial viscosity for nonlinear advection equation. Prepr. Keldysh Inst. Appl. Math. RAS 68, 1–21 (2017)

    Google Scholar 

  5. Samarskii, A.A.: The Theory of Difference Schemes. Marcel Dekker Inc., New York (2001)

    Book  Google Scholar 

  6. Kalitkin, N.N.: Chislennye metody. BHV, St.-Petersburg (2011). (in Russian)

    Google Scholar 

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Acknowledgments

This work was supported by the Russian Foundation for Basic Research (projects Nos. 16-07-00519-a, 18-07-00841-a, 16-29-15095-ofi-m).

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics of RAS, 4 Miusskaya square, 125047, Moscow, Russia

    I. V. Popov, Yu. A. Poveshchenko & S. V. Polyakov

  2. National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 31, Kashirskoe shosse, 115409, Moscow, Russia

    I. V. Popov, Yu. A. Poveshchenko & S. V. Polyakov

Authors
  1. I. V. Popov
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  2. Yu. A. Poveshchenko
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  3. S. V. Polyakov
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Corresponding author

Correspondence to I. V. Popov .

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Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Popov, I.V., Poveshchenko, Y.A., Polyakov, S.V. (2019). Construction of Higher-Order Approximation Difference Scheme for Nonlinear Convection-Diffusion Equation Using Adaptive Artificial Viscosity in Case of Two-Phase Filtering Problems. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_45

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_45

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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