### Abstract

We present the extension of the complete flux scheme to advection-diffusion-reaction systems. For stationary problems, the flux approximation is derived from a local system boundary value problem for the entire system, including the source term vector. Therefore, the numerical flux vector consists of a homogeneous and an inhomogeneous component, corresponding to the advection-diffusion operator and the source term, respectively. For time-dependent systems, the numerical flux is determined from a quasi-stationary boundary value problem containing the time-derivative in the source term. Consequently, the complete flux scheme results in an implicit semidiscretization. The complete flux scheme is validated for several test problems.
Keywords: Advection-diffusion-reaction systems · Flux (vector) · Finite volume method ·
Integral representation of the flux · Green’s matrix · Numerical flux · Matrix functions ·
Peclet matrix

Original language | English |
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Pages (from-to) | 552-568 |

Number of pages | 17 |

Journal | Journal of Scientific Computing |

Volume | 53 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2012 |

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## Cite this

Thije Boonkkamp, ten, J. H. M., Dijk, van, J., Liu, L., & Peerenboom, K. S. C. (2012). Extension of the complete flux scheme to systems of conservation laws.

*Journal of Scientific Computing*,*53*(3), 552-568. https://doi.org/10.1007/s10915-012-9588-5