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

Sofia Eriksson; Qaisar Abbas; Jan Nordström

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

Sofia Eriksson, Qaisar Abbas, Jan Nordström

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A procedure to switch 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 stable and accurate. Numerical experiments verify the theoretical accuracy for smooth solutions. In addition shock calculations is performed, using a scheme where the developed switching procedure is combined with the MUSCL technique for shock capturing.

Original language	English
Title of host publication	7th South African Conference on Computational and Applied Mechanics, SACAM 2010
Editors	Schalk Kok, Helen Mary Inglis, Daniel Nicolas Wilke
Publisher	South African Association for Theoretical and Applied Mechanics (SAAM)
Pages	128-136
Number of pages	9
ISBN (Electronic)	9780620491921
Publication status	Published - 2010
Externally published	Yes
Event	7th South African Conference on Computational and Applied Mechanics, SACAM 2010 - Pretoria, South Africa Duration: 10 Jan 2010 → 13 Jan 2010

Publication series

Name	7th South African Conference on Computational and Applied Mechanics, SACAM 2010

Conference

Conference	7th South African Conference on Computational and Applied Mechanics, SACAM 2010
Country/Territory	South Africa
City	Pretoria
Period	10/01/10 → 13/01/10

Keywords

Conservation
Finite difference methods
High order accuracy
Shock calculations
Stability
Summation-by-parts

ASJC Scopus subject areas

Computational Mechanics
Mechanical Engineering

Cite this

Eriksson, S., Abbas, Q., & Nordström, J. (2010). A stable and conservative method of locally adapting the design order of finite difference schemes. In S. Kok, H. M. Inglis, & D. N. Wilke (Eds.), 7th South African Conference on Computational and Applied Mechanics, SACAM 2010 (pp. 128-136). (7th South African Conference on Computational and Applied Mechanics, SACAM 2010). South African Association for Theoretical and Applied Mechanics (SAAM).

Eriksson, Sofia ; Abbas, Qaisar ; Nordström, Jan. / A stable and conservative method of locally adapting the design order of finite difference schemes. 7th South African Conference on Computational and Applied Mechanics, SACAM 2010. editor / Schalk Kok ; Helen Mary Inglis ; Daniel Nicolas Wilke. South African Association for Theoretical and Applied Mechanics (SAAM), 2010. pp. 128-136 (7th South African Conference on Computational and Applied Mechanics, SACAM 2010).

@inproceedings{f28e95ca459f47c192f01bc44687444c,

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

abstract = "A procedure to switch 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 stable and accurate. Numerical experiments verify the theoretical accuracy for smooth solutions. In addition shock calculations is performed, using a scheme where the developed switching procedure is combined with the MUSCL technique for shock capturing.",

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",

note = "Publisher Copyright: {\textcopyright} SACAM.; 7th South African Conference on Computational and Applied Mechanics, SACAM 2010 ; Conference date: 10-01-2010 Through 13-01-2010",

year = "2010",

language = "English",

series = "7th South African Conference on Computational and Applied Mechanics, SACAM 2010",

publisher = "South African Association for Theoretical and Applied Mechanics (SAAM)",

pages = "128--136",

editor = "Schalk Kok and Inglis, {Helen Mary} and Wilke, {Daniel Nicolas}",

booktitle = "7th South African Conference on Computational and Applied Mechanics, SACAM 2010",

}

Eriksson, S, Abbas, Q & Nordström, J 2010, A stable and conservative method of locally adapting the design order of finite difference schemes. in S Kok, HM Inglis & DN Wilke (eds), 7th South African Conference on Computational and Applied Mechanics, SACAM 2010. 7th South African Conference on Computational and Applied Mechanics, SACAM 2010, South African Association for Theoretical and Applied Mechanics (SAAM), pp. 128-136, 7th South African Conference on Computational and Applied Mechanics, SACAM 2010, Pretoria, South Africa, 10/01/10.

A stable and conservative method of locally adapting the design order of finite difference schemes. / Eriksson, Sofia; Abbas, Qaisar; Nordström, Jan.
7th South African Conference on Computational and Applied Mechanics, SACAM 2010. ed. / Schalk Kok; Helen Mary Inglis; Daniel Nicolas Wilke. South African Association for Theoretical and Applied Mechanics (SAAM), 2010. p. 128-136 (7th South African Conference on Computational and Applied Mechanics, SACAM 2010).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

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

AU - Eriksson, Sofia

AU - Abbas, Qaisar

AU - Nordström, Jan

N1 - Publisher Copyright: © SACAM.

PY - 2010

Y1 - 2010

N2 - A procedure to switch 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 stable and accurate. Numerical experiments verify the theoretical accuracy for smooth solutions. In addition shock calculations is performed, using a scheme where the developed switching procedure is combined with the MUSCL technique for shock capturing.

AB - A procedure to switch 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 stable and accurate. Numerical experiments verify the theoretical accuracy for smooth solutions. In addition shock calculations is performed, using a scheme where the developed switching procedure is combined with the MUSCL technique for shock capturing.

KW - Conservation

KW - Finite difference methods

KW - High order accuracy

KW - Shock calculations

KW - Stability

KW - Summation-by-parts

UR - http://www.scopus.com/inward/record.url?scp=84922981594&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84922981594

T3 - 7th South African Conference on Computational and Applied Mechanics, SACAM 2010

SP - 128

EP - 136

BT - 7th South African Conference on Computational and Applied Mechanics, SACAM 2010

A2 - Kok, Schalk

A2 - Inglis, Helen Mary

A2 - Wilke, Daniel Nicolas

PB - South African Association for Theoretical and Applied Mechanics (SAAM)

T2 - 7th South African Conference on Computational and Applied Mechanics, SACAM 2010

Y2 - 10 January 2010 through 13 January 2010

ER -

Eriksson S, Abbas Q, Nordström J. A stable and conservative method of locally adapting the design order of finite difference schemes. In Kok S, Inglis HM, Wilke DN, editors, 7th South African Conference on Computational and Applied Mechanics, SACAM 2010. South African Association for Theoretical and Applied Mechanics (SAAM). 2010. p. 128-136. (7th South African Conference on Computational and Applied Mechanics, SACAM 2010).

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

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this