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

A New Multidimensional Euler Scheme

by M. Fey and R. Jeltsch

(Report number 1992-09)

Abstract
A new idea is presented to solve the multidimensional Euler equations numerically. The aim of this idea is to obtain a robust shock capturing method without the use of dimensional splitting. The starting point is the idea of the one-dimensional flux vector splitting and the homogeneity of the Euler equations. Using this concept it is shown that a different interpretation of the one-dimensional waves and the use of some physical properties lead to a decomposition of the state vector into three multidimensional waves. This idea includes most of the physical properties of the Euler equations and allows infinitely many propagation directions. Assuming a Cartesian grid and constant states within each cell a numerical scheme is derived and some test calculations are shown.

Keywords: Euler equations, multidimensional waves, dimensional splitting

@Techreport{FJ92_19,
  author = {M. Fey and R. Jeltsch},
  title = {A New Multidimensional Euler Scheme},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1992-09},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1992/1992-09.pdf },
  year = {1992}
}

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).