### Abstract

We present a coarse-grained steady state solution framework for the Boltzmann kinetic equation based on a Newton-Broyden iteration. This approach is an extension of the equation-free framework proposed by Kevrekidis and coworkers, whose objective is the use of fine-scale simulation tools to directly extract coarse-grained, macroscopic information. Our current objective is the development of efficient simulation tools for modeling complex micro/nanoscale flows. The iterative method proposed and used here consists of a short Boltzmann transient evolution step and a Newton-Broyden contraction mapping step based on the Boltzmann solution; the latter step only solves for the macroscopic field of interest (e.g. flow velocity). The predicted macroscopic field is then used as an initial condition for the Boltzmann solver for the next iteration. We have validated this approach for isothermal, one-dimensional flows in the low Knudsen number regime. We find that the Newton-Broyden iteration converges in O(10) iterations, starting from arbitrary guess solutions and a Navier-Stokes based initial Jacobian. This results in computational savings compared to time-explicit integra tion to steady states when the time to steady state is longer than O(40) mean collision times.

Original language | English (US) |
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Title of host publication | Proceedings of the 4th International Conference on Nanochannels, Microchannels and Minichannels, ICNMM2006 |

Pages | 439-444 |

Number of pages | 6 |

State | Published - Dec 1 2006 |

Event | 4th International Conference on Nanochannels, Microchannels and Minichannels, ICNMM2006 - Limerick, Ireland Duration: Jun 19 2006 → Jun 21 2006 |

### Publication series

Name | Proceedings of the 4th International Conference on Nanochannels, Microchannels and Minichannels, ICNMM2006 |
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Volume | 2006 A |

### Other

Other | 4th International Conference on Nanochannels, Microchannels and Minichannels, ICNMM2006 |
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Country | Ireland |

City | Limerick |

Period | 6/19/06 → 6/21/06 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)

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## Cite this

*Proceedings of the 4th International Conference on Nanochannels, Microchannels and Minichannels, ICNMM2006*(pp. 439-444). (Proceedings of the 4th International Conference on Nanochannels, Microchannels and Minichannels, ICNMM2006; Vol. 2006 A).