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

The Method of Transport for the Euler Equations Written as a Kinetic Scheme

by S. A. Zimmermann

(Report number 1999-03)

Abstract
The Method of Transport is a genuinely multi-dimensional scheme to solve nonlinear systems of hyperbolic equations numerically. It is based on the framework of conservation laws. Here, we will consider the Euler equations. We will present an alternative formulation of the first order method based on kinetic theory. This will allow us to show that density and pressure of the numerical solution remain positive for all times. In addition, we can derive $L^1$-estimates for the numerical solution. We will also consider the second order method. This will give us more insight into the differences of the two formulations.

Keywords: Euler Equations, Multidimensional Schemes, Kinetic Schemes, Stability of Numerical Methods

@Techreport{Z99_238,
  author = {S. A. Zimmermann},
  title = {The Method of Transport for the Euler Equations Written as a Kinetic Scheme},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1999-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1999/1999-03.pdf },
  year = {1999}
}

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).