### Abstract

We present a formulation of the two-dimensional complete flux (CF) scheme in terms of local orthogonal coordinates adapted to the flow, i.e., one coordinate axis is aligned with the local velocity field and the other one is perpendicular to it. This approach gives rise to an advection-diffusion-reaction boundary value problem (BVP) for the flux component in the local flow direction. For the other (diffusive) flux component we use central differences. We will demonstrate the performance of the scheme for several examples.

Original language | English |
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Title of host publication | Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems - FVCA8 2017 |

Editors | C. Cancès, P. Omnes |

Publisher | Springer |

Pages | 437-445 |

Number of pages | 9 |

ISBN (Print) | 9783319573939 |

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 |

### Publication series

Name | Springer Proceedings in Mathematics & Statistics |
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Volume | 200 |

### 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

- Complete flux scheme
- Conservation laws
- Finite volume method
- Local orthogonal coordinates
- Numerical flux

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## Cite this

ten Thije Boonkkamp, J., Anthonissen, M., & Kwant, R. (2017). A two-dimensional complete flux scheme in local flow adapted coordinates. In C. Cancès, & P. Omnes (Eds.),

*Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems - FVCA8 2017*(pp. 437-445). (Springer Proceedings in Mathematics & Statistics; Vol. 200). Springer. https://doi.org/10.1007/978-3-319-57394-6_46