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

Access to Document

10.1016/j.jcp.2010.11.020

Cite this

@article{2fc74343989249b191fb1bbe9300f837,

title = "A stable and conservative method for locally adapting the design order of finite difference schemes",

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.",

keywords = "Conservation, Finite difference methods, High order accuracy, Shock calculations, Stability, Summation-By-Parts",

author = "Sofia Eriksson and Qaisar Abbas and Jan Nordstr{\"o}m",

year = "2011",

month = may,

day = "20",

doi = "10.1016/j.jcp.2010.11.020",

language = "English",

volume = "230",

pages = "4216--4231",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

number = "11",

}

TY - JOUR

T1 - A stable and conservative method for locally adapting the design order of finite difference schemes

AU - Eriksson, Sofia

AU - Abbas, Qaisar

AU - Nordström, Jan

PY - 2011/5/20

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

UR - https://www.scopus.com/pages/publications/79953762531

U2 - 10.1016/j.jcp.2010.11.020

DO - 10.1016/j.jcp.2010.11.020

M3 - Article

AN - SCOPUS:79953762531

SN - 0021-9991

VL - 230

SP - 4216

EP - 4231

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 11

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this