A stable and conservative method for locally adapting the design order of finite difference schemes

Sofia Eriksson; Qaisar Abbas; Jan Nordström

doi:10.1016/j.jcp.2010.11.020

A stable and conservative method for locally adapting the design order of finite difference schemes

Sofia Eriksson, Qaisar Abbas, Jan Nordström

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	4216-4231
Number of pages	16
Journal	Journal of Computational Physics
Volume	230
Issue number	11
DOIs	https://doi.org/10.1016/j.jcp.2010.11.020
Publication status	Published - 20 May 2011
Externally published	Yes

Keywords

Conservation
Finite difference methods
High order accuracy
Shock calculations
Stability
Summation-By-Parts

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2010.11.020

Cite this

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AU - Abbas, Qaisar

AU - Nordström, Jan

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Y1 - 2011/5/20

N2 - 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.

AB - 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.

KW - Conservation

KW - Finite difference methods

KW - High order accuracy

KW - Shock calculations

KW - Stability

KW - Summation-By-Parts

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ER -

A stable and conservative method for locally adapting the design order of finite difference schemes

Abstract

Keywords

ASJC Scopus subject areas

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