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A stable and conservative method for locally adapting the design order of finite difference schemes
Department of Information Technology, Scientific Computing, Uppsala University, SE-751 05 Uppsala, Sweden.
Department of Information Technology, Scientific Computing, Uppsala University, SE-751 05 Uppsala, Sweden.
Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2011 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 11, 4216-4231 p.Article in journal (Refereed) Published
Abstract [en]

A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable.

 

Numerical experiments verify the theoretical accuracy for smooth solutions. In addition, shock calculations are performed, using a scheme where the developed switching procedure is combined with the MUSCL technique.

Place, publisher, year, edition, pages
2011. Vol. 230, no 11, 4216-4231 p.
Keyword [en]
Finite difference methods; High order accuracy; Shock calculations; Conservation; Stability; Summation-By-Parts
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-67055DOI: 10.1016/j.jcp.2010.11.020ISI: 000290185000007OAI: oai:DiVA.org:liu-67055DiVA: diva2:406421
Note
Original Publication: Sofia Eriksson, Qaisar Abbas and Jan Nordström, A stable and conservative method for locally adapting the design order of finite difference schemes, 2011, Journal of Computational Physics, (230), 11, 4216-4231. http://dx.doi.org/10.1016/j.jcp.2010.11.020 Copyright: Elsevier Science B.V., Amsterdam http://www.elsevier.com/ Available from: 2011-03-25 Created: 2011-03-25 Last updated: 2013-08-30

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