The spatial and temporal evolution of the three species considered, as well as the maximum concentration levels, are correctly predicted by the model, although there is a certain lag between the analytical and numerical solutions (Figure 4). This lag is due to the numerical errors introduced by the discretization of the advective flux, which are reduced as the mesh size is refined. The mean absolute error (MAE) obtained with three different mesh sizes in combination with the first order and the Gamma schemes is shown in Table 1. Although the Gamma scheme reduces the MAE with respect to the first order scheme, in this case the effect of the mesh size clearly dominates the error on model output.

Table 1

. | . | MAE (mg/L) . | ||
---|---|---|---|---|

Δx (m)
. | Numerical scheme . | org-N . | NH_{3}-N
. | NH_{3}-N
. |

10 | First order | 0.0052 | 0.037 | 0.0145 |

5 | First order | 0.0033 | 0.0242 | 0.0095 |

2.5 | First order | 0.0025 | 0.0182 | 0.0070 |

10 | Gamma | 0.0047 | 0.0349 | 0.0134 |

5 | Gamma | 0.0031 | 0.0233 | 0.0089 |

2.5 | Gamma | 0.0023 | 0.0179 | 0.0069 |

. | . | MAE (mg/L) . | ||
---|---|---|---|---|

Δx (m)
. | Numerical scheme . | org-N . | NH_{3}-N
. | NH_{3}-N
. |

10 | First order | 0.0052 | 0.037 | 0.0145 |

5 | First order | 0.0033 | 0.0242 | 0.0095 |

2.5 | First order | 0.0025 | 0.0182 | 0.0070 |

10 | Gamma | 0.0047 | 0.0349 | 0.0134 |

5 | Gamma | 0.0031 | 0.0233 | 0.0089 |

2.5 | Gamma | 0.0023 | 0.0179 | 0.0069 |

Figure 4

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