Research reports

Years: 2025 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

Constraint preserving schemes using potential-based fluxes. II. Genuinely multi-dimensional central schemes for systems of conservation laws

by S. Mishra and E. Tadmor

(Report number 2009-32)

Abstract
We propose an alternative framework for designing genuinely multi-dimensional (GMD) finite volume schemes for systems of conservation laws in two space dimensions. The approach is based on reformulating edge centered numerical fluxes in terms of vertex centered potentials. Any consistent numerical flux can be used in defining the potentials. Suitable choices of potentials result in schemes that preserve discrete forms of interesting constraints like vorticity and divergence. The schemes are very simple to code, robust and have low computational costs. Numerical examples for scalar conservation laws, system wave equations and Euler equations of gas dynamics are presented to illustrate the efficieny the schemes.

Keywords:

@Techreport{MT09_413,
  author = {S. Mishra and E. Tadmor},
  title = {Constraint preserving schemes using potential-based fluxes. II. Genuinely multi-dimensional central schemes for systems of conservation laws},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-32},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-32.pdf },
  year = {2009}
}

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).