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

Shock tracking based on high resolution wave propagation methods

by R. J. LeVeque and K. M. Shyue

(Report number 1992-01)

Abstract
We present a simple approach to shock tracking in conjunction with conservative high resolution shock-capturing methods in one space dimension. An underlying uniform grid is used with additional grid interfaces introduced at appropriate points for tracked shocks. Conservative high resolution methods based on the large time step wave propagation approach are used on the resulting nonuniform grid. This method is stable even if some of the small cells created by the tracked interface are orders of magnitude smaller than the regular cells used to determine the time step. A fractional step method is used to handle source terms. Several calculations are presented to demonstrate the effectiveness of the method, including an unstable detonation wave calculation where mesh refinement in the reaction zone is required in addition to shock tracking. Extension of these ideas to two space dimensions is briefly discussed.

Keywords: shock tracking, finite volume methods, high resolution methods, mesh refinement.

@Techreport{LS92_11,
  author = {R. J. LeVeque and K. M. Shyue},
  title = {Shock tracking based on high resolution wave propagation methods},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1992-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1992/1992-01.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).