Skip to main content
SpringerLink
Log in

Relativistic Burgers Models on Curved Background Geometries

  • 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:

  • 1273 Accesses

Abstract

Relativistic Burgers model and its generalization to various spacetime geometries are recently studied both theoretically and numerically. The numeric implementation is based on finite volume and finite difference approximation techniques designed for the corresponding model on the related geometry. In this work, we provide a summary of several versions of these models on the Schwarzschild, de Sitter, Schwarzschild-de Sitter, FLRW and Reissner-Nordström spacetime geometries with their particular properties.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • 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

References

  1. Amorim, P., LeFloch, P.G., Okutmustur, B.: Finite volume schemes on Lorentzian manifolds. Commun. Math. Sci. 6(4), 1059–1086 (2008)

    Article  MathSciNet  Google Scholar 

  2. Ceylan, T., Okutmustur, B.: Finite volume approximation of the relativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime. Turk. J. Math. 41, 1027–1041 (2017)

    Article  MathSciNet  Google Scholar 

  3. Ceylan, T., Okutmustur, B.: Finite volume method for the relativistic Burgers model on a (1+1)-dimensional de Sitter spacetime. Math. Comput. Appl. 21(2), 16 (2016)

    MathSciNet  Google Scholar 

  4. Ceylan, T., LeFloch, P.G., Okutmustur, B.: A finite volume method for the relativistic Burgers equation on a FLRW background spacetime. Commun. Comput. Phys. 23, 500–519 (2018)

    Article  MathSciNet  Google Scholar 

  5. LeFloch, P.G., Makhlof, H., Okutmustur, B.: Relativistic Burgers equations on a curved spacetime. Derivation and finite volume approximation. SIAM J. Numer. Anal. 50(4), 2136–2158 (2012)

    Article  MathSciNet  Google Scholar 

  6. LeFloch, P.G., Okutmustur, B.: Hyperbolic conservation laws on spacetimes. A finite volume scheme based on differential forms. Far East J. Math. Sci. 31, 49–83 (2008)

    MathSciNet  MATH  Google Scholar 

  7. Nordebo, J.: The Reissner-Nordström metric. M.S. Dissertion, Department of Physics, Umea University, Switzerland (2016)

    Google Scholar 

  8. LeVeque, R.J.: Finite Volume Methods for Hyperbolic Problems, 1st edn. Cambridge University Press, Cambridge (2002)

    Book  Google Scholar 

  9. Nashed, G.G.L.: Stability of Reissner-Nordström black hole. Acta Phys. Pol. 112, 13–19 (2007)

    Article  Google Scholar 

  10. Okutmustur, B.: Propagations of shock and rarefaction waves on the Reissner-Nordström spacetimes for Burgers models. SDU J. Nat. Appl. Sci. 22(Spec. Issue), 448–459 (2018)

    Google Scholar 

  11. Wald, R.M.: General Relativity, 1st edn. The University of Chicago Press, Chicago (1984)

    Book  Google Scholar 

Download references

Acknowledgments

Supported by METU-GAP Project, Project no: GAP-101-2018-2767.

Author information

Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University (METU), 06800, Ankara, Turkey

    Baver Okutmustur

Authors
  1. Baver Okutmustur
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Baver Okutmustur .

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

Okutmustur, B. (2019). Relativistic Burgers Models on Curved Background Geometries. 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_42

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-11539-5_42

  • 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