### Abstract

We study numerically the solutions of the steady advection-diffusion problem in bounded domains with prescribed boundary conditions when the Péclet number Pe is large. We approximate the solution at high, but finite Péclet numbers by the solution to a certain asymptotic problem in the limit Pe → ∞. The asymptotic problem is a system of coupled 1-dimensional heat equations on the graph of streamline-separatrices of the cellular flow, that was developed in [21]. This asymptotic model is implemented numerically using a finite volume scheme with exponential grids. We conclude that the asymptotic model provides for a good approximation of the solutions of the steady advection-diffusion problem at large Péclet numbers, and even when Pe is not too large.

Original language | English (US) |
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Pages (from-to) | 75-92 |

Number of pages | 18 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 15 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2011 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics