Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Boundary conditions for regularized 13-moment-equations for micro-channel-flows

by M. Torrilhon and H. Struchtrup

(Report number 2008-14)

Abstract
Boundary conditions are the major obstacle in simulations based on advanced continuum models of rarefied and micro-flows of gases. In this paper we present a theory how to combine the regularized 13-moment-equations derived from Boltzmann's equation with boundary conditions obtained from Maxwell's kinetic accommodation model. While for the linear case these kinetic boundary conditions suffice, we need additional conditions in the non-linear case. These are provided by the bulk solutions obtained after properly transforming the equations while keeping their asymptotic accuracy with respect to Boltzmann's equation. After finding a suitable set of boundary conditions and equations, a numerical method for generic shear flow problems is formulated. Several test simulations demonstrate the stable and oscillation-free performance of the new approach.

Keywords:

@Techreport{TS08_379,
  author = {M. Torrilhon and H. Struchtrup},
  title = {Boundary conditions for regularized 13-moment-equations for micro-channel-flows},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2008-14},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-14.pdf },
  year = {2008}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).