### 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 language | English |
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Title of host publication | Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems |

Subtitle of host publication | FVCA 8, Lille, France, June 2017 |

Editors | C. Cancès , P. Omnes |

Place of Publication | Dordrecht |

Publisher | Springer |

Pages | 457-465 |

Number of pages | 9 |

ISBN (Electronic) | 978-3-319-57394-6 |

ISBN (Print) | 978-3-319-57393-9 |

DOIs | |

Publication status | Published - 2017 |

Event | 8th International Symposium on Finite Volumes for Complex Applications (FVCA 2017) - Lille, France Duration: 12 Jun 2017 → 16 Jun 2017 Conference number: 8 https://indico.math.cnrs.fr/event/1299/overview https://indico.math.cnrs.fr/event/1299/overview |

### Conference

Conference | 8th International Symposium on Finite Volumes for Complex Applications (FVCA 2017) |
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Abbreviated title | FVCA 2017 |

Country | France |

City | Lille |

Period | 12/06/17 → 16/06/17 |

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