### Abstract

In this paper we discuss several complete flux schemes for advection-diffusion-reaction problems. We consider both scalar equations as well as systems of equations. For the flux approximations in the latter case, we take into account the coupling between the constituent equations. We study conservation laws with discontinuous diffusion matrix/coefficient and show that the (matrix) harmonic average should be employed in the expressions for the numerical fluxes. The vectorial harmonic complete flux schemes are validated for a test problem.

Original language | English |
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Title of host publication | Numerical Mathematics and Advanced Applications 2013 (Proceedings ENUMATH'13, Lausanne, Switzerland, August 26-30, 2013) |

Editors | A. Abdulle, S. Deparis, D. Kressner, F. Nobile, M. Picasso |

Place of Publication | Cham |

Publisher | Springer |

Pages | 95-103 |

ISBN (Print) | 978-3-319-10704-2 |

DOIs | |

Publication status | Published - 2015 |

Event | conference; ENUMATH'13 - Duration: 1 Jan 2015 → … |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 103 |

ISSN (Print) | 1439-7358 |

### Conference

Conference | conference; ENUMATH'13 |
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Period | 1/01/15 → … |

Other | ENUMATH'13 |

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## Cite this

Thije Boonkkamp, ten, J. H. M., Liu, L., Dijk, van, J., & Peerenboom, K. S. C. (2015). Harmonic complete flux schemes for conservation laws with discontinuous coefficients. In A. Abdulle, S. Deparis, D. Kressner, F. Nobile, & M. Picasso (Eds.),

*Numerical Mathematics and Advanced Applications 2013 (Proceedings ENUMATH'13, Lausanne, Switzerland, August 26-30, 2013)*(pp. 95-103). (Lecture Notes in Computational Science and Engineering; Vol. 103). Springer. https://doi.org/10.1007/978-3-319-10705-9_9