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

Decomposition of the multidimensional Euler equations into advection equations

by M. Fey

(Report number 1995-14)

Abstract
Based on a genuine multi-dimensional numerical scheme, called Method of Transport, we derive a form of the compressible Euler-equations, capable of a linearization for any space dimension. This form allows a rigorous error analysis of the linearization error without the knowledge of the numerical method. The generated error can be eliminated by special correction terms in the linear equations. Hence, existing scalar high order methods can be used to solve the linear equations and obtain high order accuracy in space and time for the non-linear conservation law. In our approach, the scalar version of the method of transport is used to solve the linear equations. This method is multi-dimensional and reduces the solution of the partial differential equation to an integration process. Convergence histories presented at the end of the paper show that the numerical results agree with the theoretical predictions.

Keywords: conservation laws, flux vector splitting, characteristic surfaces

@Techreport{F95_181,
  author = {M. Fey},
  title = {Decomposition of the multidimensional Euler equations into advection equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1995-14},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1995/1995-14.pdf },
  year = {1995}
}

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).