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A Nonlinear Flux Approximation Scheme for the Viscous Burgers Equation

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Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems (FVCA 2017)

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Abstract

We present a nonlinear flux approximation scheme for the spatial discretization of the viscous Burgers equation. We derive the numerical flux function from a local two-point boundary value problem (BVP), which results in a nonlinear equation that depends on the local boundary values and the diffusion constant. The flux scheme is consistent and stable (does not introduce any spurious oscillations), as demonstrated by the numerical results.

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References

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Acknowledgements

This work is part of the Industrial Partnership Programme (IPP) Computational Sciences for Energy Research of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organization for Scientific Research (NWO).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600MB, Eindhoven, The Netherlands

    N. Kumar, J. H. M. ten Thije Boonkkamp & B. Koren

  2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany

    A. Linke

Authors
  1. N. Kumar
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  2. J. H. M. ten Thije Boonkkamp
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  3. B. Koren
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  4. A. Linke
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Corresponding author

Correspondence to N. Kumar .

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Editors and Affiliations

  1. Equipe RAPSODI, Inria Lille - Nord Europe, Villeneuve-d’Ascq, France

    Clément Cancès

  2. Commissariat à l'énergie atomique et aux énergies alternatives, Centre de Saclay, Gif-sur-Yvette, France

    Pascal Omnes

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Kumar, N., ten Thije Boonkkamp, J.H.M., Koren, B., Linke, A. (2017). A Nonlinear Flux Approximation Scheme for the Viscous Burgers Equation. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_48

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