Energy stability of the MUSCL scheme

Qaisar Abbas; Edwin Van Der Weide; Jan Nordström

Energy stability of the MUSCL scheme

Qaisar Abbas, Edwin Van Der Weide, Jan Nordström

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

Abstract

We analyze the energy stability of the standard MUSCL scheme. The analysis is possible by reformulating the MUSCL scheme in the framework of summation-by-parts (SBP) operators including an artificial dissipation. The effect of different slope limiters is studied. It is found that all the slope limiters do not lead to the correct sign of the entries in the dissipation matrix. The implication of that is discussed for both linear and nonlinear scalar problems.

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	353-360
Number of pages	8
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

Artificial dissipation
Energy estimates and numerical stability
MUSCL scheme
Summation-by-parts form

ASJC Scopus subject areas

Computational Mechanics
Mechanical Engineering

Cite this

Abbas, Q., Van Der Weide, E., & Nordström, J. (2010). Energy stability of the MUSCL scheme. In S. Kok, H. M. Inglis, & D. N. Wilke (Eds.), 7th South African Conference on Computational and Applied Mechanics, SACAM 2010 (pp. 353-360). (7th South African Conference on Computational and Applied Mechanics, SACAM 2010). South African Association for Theoretical and Applied Mechanics (SAAM).

Abbas, Qaisar ; Van Der Weide, Edwin ; Nordström, Jan. / Energy stability of the MUSCL scheme. 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. 353-360 (7th South African Conference on Computational and Applied Mechanics, SACAM 2010).

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abstract = "We analyze the energy stability of the standard MUSCL scheme. The analysis is possible by reformulating the MUSCL scheme in the framework of summation-by-parts (SBP) operators including an artificial dissipation. The effect of different slope limiters is studied. It is found that all the slope limiters do not lead to the correct sign of the entries in the dissipation matrix. The implication of that is discussed for both linear and nonlinear scalar problems.",

keywords = "Artificial dissipation, Energy estimates and numerical stability, MUSCL scheme, Summation-by-parts form",

author = "Qaisar Abbas and {Van Der Weide}, Edwin and Jan Nordstr{\"o}m",

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Abbas, Q, Van Der Weide, E & Nordström, J 2010, Energy stability of the MUSCL scheme. 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. 353-360, 7th South African Conference on Computational and Applied Mechanics, SACAM 2010, Pretoria, South Africa, 10/01/10.

Energy stability of the MUSCL scheme. / Abbas, Qaisar; Van Der Weide, Edwin; 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. 353-360 (7th South African Conference on Computational and Applied Mechanics, SACAM 2010).

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

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T1 - Energy stability of the MUSCL scheme

AU - Abbas, Qaisar

AU - Van Der Weide, Edwin

AU - Nordström, Jan

N1 - Publisher Copyright: © SACAM.

PY - 2010

Y1 - 2010

N2 - We analyze the energy stability of the standard MUSCL scheme. The analysis is possible by reformulating the MUSCL scheme in the framework of summation-by-parts (SBP) operators including an artificial dissipation. The effect of different slope limiters is studied. It is found that all the slope limiters do not lead to the correct sign of the entries in the dissipation matrix. The implication of that is discussed for both linear and nonlinear scalar problems.

AB - We analyze the energy stability of the standard MUSCL scheme. The analysis is possible by reformulating the MUSCL scheme in the framework of summation-by-parts (SBP) operators including an artificial dissipation. The effect of different slope limiters is studied. It is found that all the slope limiters do not lead to the correct sign of the entries in the dissipation matrix. The implication of that is discussed for both linear and nonlinear scalar problems.

KW - Artificial dissipation

KW - Energy estimates and numerical stability

KW - MUSCL scheme

KW - Summation-by-parts form

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M3 - Conference contribution

AN - SCOPUS:84922997131

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

SP - 353

EP - 360

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 -

Abbas Q, Van Der Weide E, Nordström J. Energy stability of the MUSCL scheme. 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. 353-360. (7th South African Conference on Computational and Applied Mechanics, SACAM 2010).

Energy stability of the MUSCL scheme

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

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