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

Entropy conservative and entropy stable finite volume schemes for multi-dimensional conservation laws on unstructured meshes

by A. Madrane and U. S. Fjordholm and S. Mishra and E. Tadmor

(Report number 2012-31)

Abstract
We present entropy stable schemes for the two-dimensional Euler equations on unstructured grids. We develop a novel energy conservative scheme that is very simple to implement, is computationally cheap and is stable compared to other existing energy conservative schemes. To allow for a correct dissipation of energy in the vicinity of shocks, a novel numerical diffusion operator of the Roe type is designed. The energy conservative scheme, together with this diffusion operator, gives an energy stable scheme for Euler equation on unstructured grids. Numerical experiments are presented to demonstrate the robustness of the proposed schemes. Numerical experiments include the Sod shock tube problem, vortex advection and flow past a NACA0012 airfoil.

Keywords:

@Techreport{MFMT12_474,
  author = {A. Madrane and U. S. Fjordholm and S. Mishra and E. Tadmor},
  title = {Entropy conservative and entropy stable finite volume schemes for multi-dimensional conservation laws on unstructured meshes},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2012-31},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2012/2012-31.pdf },
  year = {2012}
}

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).