### Abstract

We present an extension of the complete flux scheme for conservation laws containing a linear source. In our new scheme, we split off the linear part of the source and incorporate this term in the homogeneous flux, the remaining nonlinear part is included in the inhomogeneous flux. This approach gives rise to modified homogeneous and inhomogeneous fluxes, which reduce to the classical fluxes for vanishing linear source. On the other hand, if the linear source is large, the solution of the underlying boundary value problem is oscillatory, resulting in completely different numerical fluxes. We demonstrate the performance of the homogeneous flux approximation.

Original language | English |
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Title of host publication | Numerical Mathematics and Advanced Applications - ENUMATH 2015 |

Editors | B. Karasozen, M. Manguoglu, M. Tezer-Sezgin, S. Goktepe, O. Ugur |

Publisher | Springer |

Pages | 23-31 |

Number of pages | 8 |

ISBN (Electronic) | 978-3-319-39929-4 |

ISBN (Print) | 978-3-319-39927-0 |

DOIs | |

Publication status | Published - 2016 |

Event | 2015 European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2015) - Middle East Technical University, Ankara, Turkey Duration: 14 Sep 2015 → 18 Sep 2015 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering (LNCSE) |
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Publisher | Springer |

Volume | 112 |

### Conference

Conference | 2015 European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2015) |
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Abbreviated title | ENUMATH 2015 |

Country | Turkey |

City | Ankara |

Period | 14/09/15 → 18/09/15 |

## Cite this

ten Thije Boonkkamp, J. H. M., Rathish Kumar, B. V., Kumar, S., & Pargaei, M. (2016). Complete flux scheme for conservation laws containing a linear source. In B. Karasozen, M. Manguoglu, M. Tezer-Sezgin, S. Goktepe, & O. Ugur (Eds.),

*Numerical Mathematics and Advanced Applications - ENUMATH 2015*(pp. 23-31). (Lecture Notes in Computational Science and Engineering (LNCSE); Vol. 112). Springer. https://doi.org/10.1007/978-3-319-39929-4_3