Construction of Higher-Order Approximation Difference Scheme for Nonlinear Convection-Diffusion Equation Using Adaptive Artificial Viscosity in Case of Two-Phase Filtering Problems | SpringerLink
Skip to main content
Springer Nature Link
Log in

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

  • Conference paper
  • First Online:
Finite Difference Methods. Theory and Applications (FDM 2018)

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

Included in the following conference series:

  • 1397 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

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 

Download references

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).

Author information

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. A. Poveshchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. V. Polyakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. V. Popov .

Editor information

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

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation