Acceleration methods for coarse-grained numerical solution of the boltzmann equation

Husain A. Al-Mohssen, Nicolas G. Hadjiconstantinou, Ioannis G. Kevrekidis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationProceedings of the 4th International Conference on Nanochannels, Microchannels and Minichannels, ICNMM2006
Pages439-444
Number of pages6
StatePublished - Dec 1 2006
Event4th International Conference on Nanochannels, Microchannels and Minichannels, ICNMM2006 - Limerick, Ireland
Duration: Jun 19 2006Jun 21 2006

Publication series

NameProceedings of the 4th International Conference on Nanochannels, Microchannels and Minichannels, ICNMM2006
Volume2006 A

Other

Other4th International Conference on Nanochannels, Microchannels and Minichannels, ICNMM2006
CountryIreland
CityLimerick
Period6/19/066/21/06

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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  • Cite this

    Al-Mohssen, H. A., Hadjiconstantinou, N. G., & Kevrekidis, I. G. (2006). Acceleration methods for coarse-grained numerical solution of the boltzmann equation. In 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).