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

Boundary Treatment for a Cartesian Grid Method

by H. Forrer

(Report number 1996-04)

Abstract
We are interested in a numerical solution to the Euler Equations in complicated 2-dimensional geometries using a Cartesian grid method. To avoid stability problems or loss of accuracy along the boundary, this requires a special treatment of the irregular cells along the boundary. In this paper we present a new technique for the boundary treatment. The technique is built upon a high resolution finite volume method with dimensional splitting. To avoid stability problems for small boundary cells due to instable fluxes, we use an enlargement of the domain of dependence. The enlarged domains may lie beyond the boundary. By a local mirroring at the boundary we determine values of the flow variables also for these regions. This enables us to calculate stable fluxes for the small boundary cells. These fluxes are formally of second order accuracy. Among other examples we calculate a Prandtl-Meyer expansion, a double Mach reflection and a shock diffraction by a pair of cylinders. The latter example points to a major advantage of Cartesian grid methods, the ability to cope with complicated geometries.

Keywords:

@Techreport{F96_187,
  author = {H. Forrer},
  title = {Boundary Treatment for a Cartesian Grid Method},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-04},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-04.pdf },
  year = {1996}
}

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).