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

Stable finite difference schemes for the magnetic induction equation with Hall effect

by P. Corti and S. Mishra

(Report number 2011-23)

Abstract
We consider a sub-model of the Hall-MHD equations: the so-called magnetic induction equations with Hall effect. These equations are non-linear and include third-order spatial and mixed derivatives. We show that the energy of the solutions is bounded and design finite difference schemes that preserve the energy bounds for the continuous problem. We design both divergence preserving schemes and schemes with bounded divergence. The schemes are compared on a set of numerical experiments that demonstrate the robustness of the proposed schemes.

Keywords:

@Techreport{CM11_97,
  author = {P. Corti and S. Mishra},
  title = {Stable finite difference schemes for the magnetic induction equation with Hall effect },
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-23},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-23.pdf },
  year = {2011}
}

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).