A nonlinear flux approximation scheme for the viscous burgers equation

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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.

Original languageEnglish
Title of host publicationFinite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems
Subtitle of host publicationFVCA 8, Lille, France, June 2017
EditorsC. Cancès , P. Omnes
Place of PublicationDordrecht
PublisherSpringer
Pages457-465
Number of pages9
ISBN (Electronic)978-3-319-57394-6
ISBN (Print)978-3-319-57393-9
DOIs
Publication statusPublished - 2017
Event8th International Symposium on Finite Volumes for Complex Applications (FVCA 2017) - Lille, France
Duration: 12 Jun 201716 Jun 2017
Conference number: 8
https://indico.math.cnrs.fr/event/1299/overview
https://indico.math.cnrs.fr/event/1299/overview

Conference

Conference8th International Symposium on Finite Volumes for Complex Applications (FVCA 2017)
Abbreviated titleFVCA 2017
CountryFrance
CityLille
Period12/06/1716/06/17
Internet address

Keywords

  • Nonlinear local BVP
  • Numerical flux
  • Viscous burgers equation

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  • Cite this

    Kumar, N., ten Thije Boonkkamp, J. H. M., Koren, B., & Linke, A. (2017). A nonlinear flux approximation scheme for the viscous burgers equation. In C. Cancès , & P. Omnes (Eds.), Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017 (pp. 457-465). Dordrecht: Springer. https://doi.org/10.1007/978-3-319-57394-6_48